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By I. S. Levy, J. L. Brimhall, B. Mastel

Specimens of' Hastelloy X-280, a low-cobalt version of the solid-solution- hardened nickel-base alloy Hastelloy X, were given a series of thermomechanical treatttzents. They were then Lensile-tested at room temperature and 1350°F. The Microstructures of the specimens tested at 1350°F were studied by electron Microscopy. Microscopy showed that dislocation tangling, caused by the cold working, mas still in evidence after aging-for 24 hr to temperatures as high as 1550oF. (Cr, Mo)23 C6, (Fe, Mo)6 C'. as well us an unidentifiable phase precipitale due to the combination of the thermomechanical treatments and subsequent tensile strain. The room -temperature and 1350°F tensile properties show a general increase ill strength and decreccse in ductility with increusing cold-work level. This is due to the dislocation taangling-. PerLurbatiot~s to this general trend occur- due to solid-solution weakening at the higher cold-work levels as a direct result of the preciplitation reactions. THE requirements for corrosion resistance and high-temperature strength place nickel-base alloys among the more promising materials for advanced nuclear reactor applications. However, when these alloys are irradiated at service temperatures, they generally suffer severe embrittlement'" and reduction in rupture life.3 Certain experimental treatments resulted in improvements in the tensile and stress-rupture properties of Hastelloy X-280, a solution-hardened nickel-base alloy.' To provide a basis for understanding these improvements, unirradiated tensile specimens were examined by electron microscopy. The results are reported in this paper. EXPERIMENTAL DETAILS Material. Hastelloy X-280, a low-cobalt version of Hastelloy X, is a member of the solution-hardened class of nickel-base alloys. The Hastelloy X-280 was obtained from 4- and 1-in: thick plates in the mill -annealed condition. Table I gives the chemical composition of the material as reported by the National Spectrographic Laboratories. ~x~erimental Treatments. Plates of suitable size, 12 by 3 by 1 in., or by + in., were cut under a water jet from the stock material and examined ultrasonic -ally for homogeneity of grain size and absence of voids. The acceptable plates were solution-treated at 2150°Ffor 1 hr and air-cooled. These plates were then reduced in thickness by cold rolling 0, 10, 15: or 20 pct along the original rolling direction. The plates were machined into buttonhead tensile specimens with a gage diameter of 0.125 in., with a gage length of 1.125 in., and with their tensile axes parallel to the rolling direction. The specimens were examined for quality of finish with a penetrant dye, ultra son ically checked for voids, and finally given a dimensional tolerance check with an optical comparator. The acceptable specimens were aged for 24 hr at either 1000" or 1500 F and air-cooled. These specimens were then held at 540°F in a water loop for approximately 18 days to qualify as controls for similar specimens irradiated under the same conditions of time, temperature, water chemistry, and flow rate. Table U summarizes the treatments. These treatments were investigated to establish whether prior precipitation and stabilization of carbide phases at strain sites within the matrix could reduce the amount of carbides available for precipitation at grain boundaries during service. Tensile-Test Conditions. Specimens were tested to fracture at room temperature or 1350 F in air on an Instron tensile-testing machine at a crosshead speed of 0.05 in. per min. The time for the furnace to reach equilibrium at 1350°F was approximately 30 min; soak time prior to testing was 15 min; and test duration was approximately 5 min.

Jan 1, 1968

By J. B. Morgan

The mechanical behavior of MgCu2 from 20 o to 725°C has been determined by "brittle-ring" tensite-test techniques, axial compression, and bending experiments. Compressive ductility begins at 450°C (0.65 T/Tm) and slowly increases with increasing temperature white the tensile ductility is characterized by an abrupt brittle-ductile transition at 600°C (0.8T/Tm). The compressive strength increases eightfold from room temperature to 400°C with a "normal" decrease as the temperature is further increased. The tensile strength goes through a rather abrupt threefold increase above 600°C with a subsequent decrease at higher temperatures. The slip system is (111)[110] and the twinning system is (111)[112]. At high temperatures MgCu2 is quite rate-sensitive, and dynamic yield points are observed that are extremely orientation-dependent. The high-temperature creep behavior under constant load is characterized by an increasing strain-rate with time. The general characteristics of the mechanical behavior make it possible to classify MgCu2 with those materials in which initial mobile dislocation density and the dislocation velocity-stress dependence are significant in determining mechanical response. Mgcu2 is the C15 prototype of the cubic Laves phase. Its range of homogeneity extends from 32.8 to 35.5 at. pct Mg at 500°C and narrows at lower temperatures. The lattice parameter is reported to vary from 7.02 to 7.05A,1 and the compound is completely ordered to the melting point of 819°C. MgCu2 has a brassy metallic appearance, is extremely brittle, and many of its physical properties are intermediate between those of the constituent elements: the electrical resistivity is 3.5 x 10-6 ohm-cm, Young's modulus is 10x 106 psi, the shear modulus is 6 x l06 psi, and the thermal coefficient of expansion is 18.7 x 10-6 cm per cm per "C from 20" to 250°C. Usually, properties of intermetallic compounds as functions of temperature have been determined by hardness, compression, or impact behavior, and almost all of these experiments have been performed on polycrystalline materials. Tammann and Dahl,2 for instance, determined the onset of ductility in a series of binary intermetallics by ball-hardness measurements and found the onset to range between 0.71 and 0.96 T/T,. Lowrie's3 investigations included some tensile properties, and he found ductility beginning around 0.65 T/Tm for most materials examined. His work did include some data on polycrystalline, nonstoichiometric MgCu2, however. The present work is an attempt to extend the examination of the particular compound MgCu2 in single-crystal form in order to aid the formation of general concepts about mechanical be-

Jan 1, 1965

By W. D. Robertson, E. G. Grenier, V. F. Nole

The electrical, mechanical, and corrosion cracking properties of an age-hardenable Cu-Ni-Si alloy have been studied over a range of time, temperature, and deformation states for the purpose of determining the relationship between the properties and the structural state. The precifitate has been identi3ed as and the sites of preferred precipitation have been located by electron microscope studies of the structures developed by various combinations of heat treatment and plastic deformation. An extreme form of deformation banding has been observed in the aged alloy that results in high strain concentration in bands lying parallel to {111} planes. These bands are the structural paths along which transcrys-talline cracks propagate in the deformed alloy. The observations provide a basis for a general mechanism of transgranu-lar corrosion cracking of face-centered cubic alloys in terms of stacking fault probability. AMONG the age-hardening copper alloys the copper-nickel-silicon (Silnic Bronze) type is outstanding in exhibiting a high strength combined with a considerable capacity for cold working, a relatively high conductivity, and a low to negligible susceptibility to stress corrosion cracking. It is not a new alloy and it has been the subject of a number of investigations,1-5 which were made primarily to establish practical composition and heat treatment limits. The structural characteristics of the aging processes in this alloy have not previously been studied in detail. This particular investigation was undertaken to explore, in detail, and over a wide range of conditions, the properties obtainable by various combinations of working and heat treatment and to correlate structural changes with the observed mechanical, electrical and corrosion properties. MATERIAL AND PROCESSING Eight different commercial heats of the alloy were made and used in the investigation. The range of composition among the eight heats is shown in Table I. Billets, 8 by 24 in., were cast into water-cooled molds, extruded to 1.687-in. rod, and quenched in water after extrusion. Extruded material was rod rolled to 0.750 in., annealed at 1450° F for 2.5 hr, and quenched in water. Subsequent working operations were performed by tandem rolling to various sizes depending on the degree of reduction required. Final cold-working operations were performed by drawing to a uniform size of 0.187 in. diam and straightening by a roller straightening machine (Lewis). The combinations of heat treatment, working and aging that were investigated are summarized in Table 11; the various treatments were performed in the order given in each row of the table, and they will be subsequently identified by the symbols shown in the first column. SOLUTION TREATMENT All material investigated in the cold-worked condition, or cold worked prior to aging, was solution

Jan 1, 1962

By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.' If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By F. W. Jessen, John C. Miller

In many areas where carbonate rocks form important parts of the stratigraphic sequence, stratigraphers have experienced varying degrees of difficulty in differentiating and correlating limestone and dolomite units in both surface and subsurface work. With early Paleozoic rocks of the Mid-Continent, insoluble residues yield a remarkable amount of strati-graphic data and relatively good correlations may be carried over broad distances.' Unfortunately, neither such information nor electric logs and radioactive logs have been particularly helpful in interpreting the limestone sections of the Permian Basin of West Texas. This is because: (1) the variations in the sections may be very slight; (2) no completely satisfactory method of interpretation has been developed; and (3) the measurements themselves are not sensitive enough for small variations. Also, such logs are influenced by the fluid content. Paleontology and micro-paleontology remain the ultimate arbiters. As a routine tool, however, paleontol-ogical examination is slow and tedious. Chemical analysis may be used, but this, too, is extremely slow. Although rocks are not classified according to chemical composition, there is considerable variation with rock types. Correlation by chemical composition has two advantages, first, the characteristics determined are subject to minimum human error and interpretation, and secondly, the lithologic changes are not masked by fluid content as in the case of electric and radioactive logs. Some fossils concentrate certain elements which tentatively might be used to date rock units.' Rapid chemical analysis by spec-trographic means could be used as an adjunct to other means employed in correlation work, or might, in itself, present a suitable method. PURPOSE OF THIS INVESTIGATION Sloss and Cooke' have published data concerning spectrographic analysis of limestone rocks specifically for purposes of direct correlation of a single formation. These authors found satisfactory evidence that differences in percentage of four elements (Mg, Fe, Al, and Sr) in the Mississippian limestones of northern Montana were useful in carrying out correlation of this formation over a distance of approximately 50 miles. It was concluded from the preliminary work that the spectrochemical method offered possibilities of solution of some problems of correlation heretofore not possible. Since the work of Sloss and Cooke' was confined to one particular limestone zone, extension of the use of the method to examine two or more geologic formations would aid materially in the over-all problem of correlation of such rocks. Equipment is now available commercially with which very rapid spectrographic analyses may be made, and hence the problem was to determine whether the variations existing in the minor constituents of limestones were sufficient for use in possible correlation. Qualitative and semi-quantitative investigations were made to determine whether significant changes in the chemical condition occurred. It was a further purpose to investigate the geologic time-boundaries to see whether significant chemical variation could be found corresponding to the paleontological breaks. It was desirable to attempt correlation of a thick section of limestone or dolomite rock and to have as much information as possible on the section. Furthermore, it was felt that examination of formations more difficult to correlate by other means would enhance the value of the method should definite points of correlation be found. Samples were chosen from the Chapman-McFarlin Cogdell No. 25 well in the Cogdell field, Kent County, Tex., and from the General Crude Oil Co., Coleman No. 193-2 well in the Salt Creek field, Kent County, Tex. These fields belong to the famous series of "Canyon" reef fields of West Texas. Cores from the above wells were available from the United States Geological Survey, Austin, Tex. THE SPECTROGRAPHIC METHOD The choice of procedure to be followed in this investigation was based on the anticipated requirements peculiar to the problem. Since the problem was primarily to investigate the possibilities of applying the spec-trograph to problems of correlation in thick carbonate sections, a precise quantitative analysis did not appear necessary. A qualitative analysis to show the possible absence of presence of any element, or a semi-quantitative analysis of the elements present to show the relative changes in magnitude of selected elements was required. Both types of analysis were employed. The two most widely applied methods of semi-quantitative estimates are those of Harvey and of Slavin4,5 though various other procedures have been described.6 while the Harvey method has been modified by Addink,7 this refinement did not seem necessary to the present problem. Essentially, the procedure employed is a variation of the total energy method of Slavin with two exceptions: (1) stressing matrix effect, and (2) using densitometer measurements. As measured by a densito-

Jan 1, 1956

By H. C. Gatos, A. D. Kurtz

WITH the growing interest in the mechanism of self-diffusion of metals, the study of accurate and convenient methods for determining self-diffu-sion coefficients appears highly desirable. It was with this objective in mind that the present investigation was undertaken. Gatos and Azzam1 employed an autoradiographic technique for measuring self-diffusion coefficients of gold. This method involved sectioning of the specimen through the diffusion zone and recording the radioactivity directly on a photographic film. Because of the very short range of the emitted ß rays in gold, the activity recorded on the film was essentially the true surface activity. With proper choice of the sectioning angle, sufficient resolution could be obtained and the entire concentration-distance curve recorded in one measurement. For the boundary conditions of the experiment, where an infinitesimally thin layer of radioactive material diffuses in positive and negative directions into the end faces of a rod of infinite length, the solution of the diffusion equation is C/Cn = 1/v4pDt exp (-x2/4Dt) where C is the concentration of diffusing element (photographic density in this case), C,, is the constant (depending upon amount of radioactive material), x is the diffusion distance, D is the diffusion coefficient, and t is the time. Thus, by plotting the logarithm of the concentration vs the square of the diffusion distance, a straight line results and the slope contains the diffusion coefficient. In this manner, the self-diffusion coefficient of gold can be obtained as a function of temperature. In the present investigation the results reported by Gatos and Azzam1 have been verified, and the autoradiographic technique has been further developed and applied for the determination of the self-diffusion coefficient of gold at a number of temperatures. Furthermore, the energy of activation for the self-diffusion of gold has been conveniently determined. . Experimental Techniques Preparation of Specimens: The inert gold of high purity was received in the form of a rod from which cylinders were cut and machined to a diameter of 0.500 in. The specimens were annealed to a suitably large grain size and the faces were surface ground prior to the deposition of the radioactive layer. The radioactive isotope Au198 was chosen. It was produced in the Brookhaven pile by means of the reaction Au197 + n ? Au108. It decays by ß emission (0.96 mev) to Hg108 with the subsequent emission of a y ray (0.41 mev). 70Au 108 ? 80Hg 108 + -1e°. The half life of the Au108 is 2.7 days so that a strict time schedule had to be maintained in order to secure sufficient activity until the end of the experiments. For this reason, initial activities as high as 10,000 millicuries per gram were used. The gold arrived in the form of foil and was evaporated onto one face of each gold specimen cylinder to a thickness of about 100A. A sandwich-type specimen was formed by welding two such cylinders together. Evaporation of Gold: The gold was evaporated under vacuum from heated tantalum strips which were bent in such a way as to limit the solid angle through which the gold was allowed to vaporize, thus insuring a more efficient utilization of the gold. The specimens rested on flat brass rings which had an inner diameter of 0.475 in. The entire specimen-holding assembly could be manipulated from outside the vacuum system by means of a magnet which attracted a slug of soft iron attached to the assembly. By evaporating inert gold on glass slides under conditions identical to those employed for the radioactive gold, it was found that the thickness of the films was about 100A. Welding: The welding was performed by hot pressing in a stainless steel cylinder. The inside of the cylinder was threaded and fitted for two plugs. The specimens to be welded were placed in the middle of the cylinder and two pressing disks, one at each end, were inserted to avoid shearing stresses as the plugs were tightened. Mica disks were placed between the pressing disks and the specimens to prevent them from welding. The plugs were then tightened with a hand wrench and the entire unit was placed in an argon stream for about an hour to remove the oxygen. The unit was then inserted in the center of an argon atmosphere furnace maintained at about 700°C and left there for about an hour. Because of the difference in the temperature coefficient of expansion of the two metals, as the temperature rose. the pressure on the specimen-rollple increased and a weld resulted Welding was generally satisfactory under the conditions described.

Jan 1, 1955

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By Robert E. Green, Wolfgang Sachse

Simullaneous ultrasonic attenuation measurements of both quasishear waves propagating in single cryslals of aluminum indicate that, in the undeformed annealed state, the dislocation density is generally not uniform on all slip systems. Change oof attenuation measurements made during plastic defortnation of crystals , which possessed specific orientations ideal for studying the orientation dependence of dislocation damping, indicate that, for low strain levels, dislocation motion occurs on additional slip systems besides the primary one, even for crystals oriented for plastic deformation by single slip. THE sensitivity of internal friction measurements permits such measurements to be used successfully in studying the deformation characteristics of metal crystals. On the basis of experimental observations, T. A. Read1 was the first to associate internal friction losses with various dislocation mechanisms. Since that time further work2-' has been performed and a dislocation damping theory has been formulated by Granato and Lucke.6 In the amplitude independent region, this theory predicts the attenuation a to be dependent on an orientation factor O, a dislocation density A, and an average loop length L. if is a constant, independent of crystallographic orientation. For a given crystallographic orientation, changes in dislocation density and loop length give rise to the observed attenuation changes accompanying plastic deformation. The Granato-Liicke theory suggests the investigation of the orientation dependence of attenuation measurements in hopes of obtaining information to separate dislocation motion losses from other losses.7 An experimental study of the orientation dependence of attenuation in undeformed annealed single crystals should yield an insight into the uniformity of dislocation distribution throughout the entire specimen. A similar study on crystals plastically deformed in a prescribed fashion should give information about the alterations in the dislocation distribution on the slip systems activated during plastic deformation. The possible modes of elastic waves which can be propagated in aluminum,8 copper,9 zinc,10 and other hexagonal metals" have been calculated. Associated with each mode of wave propagation are dislocation damping orientation factors, which are based on the resolution of the stress field of that particular elastic wave onto the various operative slip systems in the material. These orientation factors have also been calculated as a function of crystallographic orientation in the papers cited above. Einspruch12 obtained agreement between predicted and observed attenuation values of longitudinal and shear waves in (100) and (110) directions of two undeformed aluminum crystal cubes. He ascribed the slight deviations between predicted and observed values to a nonuniform dislocation distribution, or to other loss mechanisms. In shear deformation of zinc crystals, Alers2 found that the attenuation of shear waves having their particle displacements in the slip plane was very sensitive to the deformation, while the longitudinal wave attenuation was affected only when the wave propagation direction was not normal to the slip plane. Using aluminum single crystals oriented for single slip, Hikata3 et al. found that during tensile deformation the change of attenuation of the shear wave (actually quasishear) having particle displacements nearly perpendicular to the primary slip direction exhibited the easy-glide phenomena, while longitudinal waves did not. Similar results were reported by Swanson and Green5 during compressive deformation of aluminum crystals. These results are in qualitative agreement with the calculated orientation factors for specimens of this orientation. In well-annealed, undeformed aluminum crystals, the damping is expected to be due to dislocations vibrating on all twelve slip systems. The orientation factors associated with this initial damping will be designated by O2 and O3, where a, represents the average orientation factor for the slow shear (or quasishear) wave and O3 represents the average orientation factor for the fast shear (or quasishear) wave. The calculation of these values for aluminum crystals by Hinton and Green8 shows that they vary very little as a function of crystallographic orientation—at most, by a factor of 2.47. If the dislocation density and loop length are uniform, then in the initial undeformed state, Here the subscript zero refers to the initial value of the attenuation. Also for aluminum, the calculations8 show that the orientation factors for primary slip only, associated with each shear wave, exhibit a sharp minimum for particular crystallographic orientations. A composite plot of the two shear wave orientation factors for primary slip only is shown in Fig. 1. Since these orientation factors are associated with dislocation motion occurring on the primary slip system only, the proper condition to check these factors might be attained by slightly deforming a single crystal oriented for primary slip. For dislocation motion on the primary slip system only,

Jan 1, 1969

By R. D. Daniels, T. W. Wood

The tensile properties of columbium and Cb-H alloys containing up to 455 ppm H were studied as a function of temperature and strain rate. Hydrogen, introduced into columbium at elevated temperatures, using a thermal -equilibrium technique, embrittled columbium most severely at about —77°C. This elnbrittle ment occurred even at hydrogen concentrations of an order of 20 ppm. At higher temperatures, the hydrogen tolerance of columbium increased in relation to the increased solubility of hydrogen in tile metal. Below this temperature hydrogen tolerance, as determined by ductility and fracture stress, increased slightly. Strain rate had little effect on the tensile results for cross-head speeds over the range 0.002 to 2.0 in. per min. Strain aging during the tensile test appears to explain the ductility mininmum at —77°C. The apparent increase in hydrogen tolerance at lower temperatures is attributed to the low mobility of hyhogen. Experiments were performed in which samples were prestrained in tension at room temperature and tested to failure at —196°C. Results suggest that hydrogetz segregation to preformed crack nuclei can cause subsequent embrittlement even at temperatures where hydrogen mobility is too low to cause embrittlement in a normal tensile test. COLUMBIUM is an example of the class of bcc metals with ductile-brittle transition temperatures sensitive to the presence of interstitial atom contaminants. Hydrogen is one of these embrittling contaminants. The embrittling effect of hydrogen is less potent, perhaps, in columbium than in some of the other bcc refractory metals, but it is still a problem of both theoretical and practical interest. Unlike hydrogen in iron and steels, hydrogen in columbium is exothermically rather than endo-thermically occluded. The embrittlement process in exothermic systems has not been studied as extensively as that in endothermic systems, especially at hydrogen concentrations below the limit of solubility. The purpose of this investigation was to evaluate the embrittlement process in initially pure columbium as a function of hydrogen content, temperature, and strain rate. The Cb-H phase diagram, according to Albrecht et al.,1 is shown in Fig. 1. Columbium reacts exothermically with hydrogen producing a solid solution at concentrations of less than about 250 ppm (parts per million by weight) H at room temperature. At concentrations above the highly temperature-dependent solvus a second phase is formed. Like many similar hydrogen-metal systems,2 his system exhibits a miscibility gap with respect to hydrogen solution. Albrecht found the critical temperature of the miscibility gap to be about 140°C, the critical concentration to be 0.23 atom fraction hydrogen, and the critical pressure to be 0.01 mm Hg. Above 140°C there is a solid solution of increasing lattice constant extending across the phase diagram. Hydrogen concentrations of particular interest in this investigation were those below the limit of solubility in columbium. At hydrogen concentrations above the limit of solubility, columbium will contain the hydrogen-rich second phase and will be brittle under most testing conditions because the hydride generally precipitates as platelets with coincident matrix lattice strains.1'3 At hydrogen concentrations below the limit of solubility, the tensile behavior of columbium is expected to be more sensitive to the interrelationships between hydrogen concentration and mobility and the testing variables such as temperature and strain rate. Literature references to the hydrogen embrittlement of metals, especially ferrous alloys and titanium alloys, are too voluminous to mention. It is only recently, however, that detailed studies of the hydrogen embrittlement of columbium have been undertaken. Wilcox et a1.4 studied the strain rate and temperature dependences of the low-temperature deformation behavior of fine-grained are-melted columbium (1 ppm H) and the effect of hydrogen content (1,9, and 30 ppm H) on the mechanical behavior of columbium at a series of temperatures for a single strain rate. A strain-aging peak was ob-served at about -50°C which was attributed to the presence of hydrogen in the metal. Eustice and carlson5 studied the effect of hydrogen on the ductility of V-Cb alloys at a series of temperatures over the range -196° to 25°C. Pure columbium was embrittled by 20 ppm H which produced a ductility transition at approximately -70°C. Ingram et al.6 studied the effect of oxygen and hydrogen on the tensile properties of columbium and tantalum. A minimum in the notched-to-unnotched tensile ratio of hydrogenated columbium was obtained at about -75°C, but because of the relatively large hydrogen content employed (200 and 390 ppm) the ductility

Jan 1, 1965

By F. Claisse, R. Angers

Self-diffusion in iron has been measured during rapid a-r transformations using a variant of the Kryukou and Zhukhovitskii diffusion method. The study was performed by thermally cycling iron foils (1 to 6 cpm) through the transformation (=910°C). Some foils have been subjected to over 1000 cycles and some have spent more than 15 pct of their total diffusion time in the process of transformation. The experimental results show that the a-r transformation has no measurable effect on self-diffusion in iron. The study is completed by a quantitative analysis of mechanisms which can affect the diffusion rate during the transformation. The analysis confirms the experimental results. SINCE diffusion is an important factor in many solid-state transformations, it is of interest to study how it is affected by the stresses generated during these transformations. Clinard and Sherby1'2 were the first to make a study along these lines. They measured diffusion coefficients in Fe-FeCoV couples subjected to slow thermal cycling (1.5 cph) through the a-r transformation range. They found an enhancement of diffusion by a factor of about two. The purpose of the present paper is to report measurements of the self-diffusion coefficient of iron during much more rapid thermal cyclings (1 to 6 cpm) through the a-r transformation (-910°C). These more rapid cyclings produce higher strain rates during the transformation and should emphasize any possible influence of transformation upon diffusion. EXPERIMENTAL Iron foils, 25 to 35 µ thick, were cold-rolled from 99.92 pct pure iron and annealed in pure helium for 2 hr at 870°C; the resulting grain diameter was about 150 µ. Specimens 0.5 by 8 cm were cut from the foils and I7e55 was vapor deposited on one of their surfaces. A 38 gage alumel-chrome1 thermocouple was spot welded in the middle of one of the specimen long edges, Fig. 1. Two 38 gage chrome1 wires were also spot welded along the same edge on each side of the thermocouple; they were placed 2.5 cm apart and used for electrical resistance measurements. In order to prevent twisting and crumpling, the specimens were pinched between two quartz plates 0.1 by 1 by 7 cm and the assembly was close fitted into a 1 cm ID quartz tube. Four holes were drilled through the tube to let the 38 gage wires out: these were connected to the recording equipment by means of extension wires. 20-gage nickel wires fixed at both ends of the specimens were used to thermally cycle the foils by Joule heating. The above described device was placed in a 2.7 cm ID quartz tube which in turn was placed in a tubular furnace. Either a pure helium atmosphere or circulating hydrogen was used during the experiments. Specimens were subjected to thermal cycles between a minimum temperature To and a maximum temperature Tm at rates ranging from 1 to 6 cpm. This was obtained by maintaining the furnace at a constant temperature near the minimum temperature To and periodically passing an electric current through the specimen. Cooling was achieved by heat losses to the surroundings. The forms and periods of cycles were varied from one specimen to another; however, each specimen was subjected to one type of cycle only. The temperature and electrical resistance variations of the specimens were recorded as a function of time. The temperature curves were used for diffusion calculations while the electrical resistance curves were used to monitor the transformation and to determine its starting point and its approximate duration. Diffusion was measured by the method developed by Kryukov and zhukhovitskii3 and modified by Angers and Claisse.4,5 In this method a metallic foil is coated on one side with a radioactive isotope and the activity is measured periodically on both sides during the diffusion anneal. The following equation then holds: where: I1 Activity on the surface on which the deposit is made. I, Activity on the opposite surface. t Diffusion time. B Constant. D Diffusion coefficient. d Foil thickness including the deposit. G(t) A function of time; it is a second order correction term which is given graphically in Refs. 4 and 5. The diffusion coefficient D is found by plotting ln[(Il - I2)/(I1 + I,)] -G(t) against t; the resulting slope m leads to an accurate calculation of D through Eq. [2]. The effect of the a-r transformation on diffusion is expressed by the ratio DT/DU where:

Jan 1, 1970

By N. J. Grant, A. W. Mullendore, Y. Ishida

Creep tests were performed at 500°F on polished specimens of A1-3 pct Cu at stresses of 2000, 4000, and 6000 psi. The effects of the size and distnbution of the second phase were studied in connection with the mechanisms of deformation, especially grain boundary sliding. Although the amount of grain boundary sliding varied considerably for the different heat treatments, yestriction of grain boundary sliding is not due primarily to precipitate on the grain boundary. NUMEROUS prior investigations of grain boundary sliding, notably those of McLean, 1 Rachinger, 2 Rhines, Bond, and Kissel, 3 and Brunner and Grant,4 have established the importance of this phenomenon in the deformation of pure aluminum and its solid-solution alloys at elevated temperatures. An extension of this kind of study to the case of a simple two-phase structure is an important step towards understanding the deformation behavior of more complex alloys. A two-phase A1-3 pct Cu alloy was selected for this study. The creep behavior of alloys in this system has been studied by Sully and Hardy,5 by Underwood, Marsh, and Manning,' and by Pelloux, Chaudhuri, and Grant.7 In these studies, the prior heat treatments were such that some precipitation took place during the tests in most cases. Pelloux, Chaudhuri, and Grant7 studied the creep of A1-2 and 3 pct Cu alloys in the overaged condition. Their results indicated that the structure most effective in promoting high-temperature strength consisted of a fine, closely spaced grain precipitate and large, widely spaced particles on the grain boundary. The present work consists of quantitative meas- urements of grain boundary sliding during creep of an A1-3 pct CU alloy with four different precipitate distributions. The aims were to quantitatively define the role of the second phase on grain boundary sliding, and to obtain information regarding the mechanism of grain boundary sliding. MATERIALS AND PROCEDURE A high-purity A1-3 pct Cu alloy, kindly supplied by Alcoa, was used in this investigation. The composition of the alloy in weight percent was as shown in Table I. This composition is such that A12Cu exists as a second phase at temperatures below 850°F. A homogeneous grain size of 0.6 to 0.8 mm was obtained by annealing the machined test bars for 5 min at 1000°F, furnace cooling to 930°F, and homogenizing for 5 hr. Following the recrystalli-zation and homogenizing anneal, four different heat treatments shown in Fig. 1 were utilized. The F7 and F5 treatments utilize a furnace cool to the aging temperature while Q7 and Q5 have a water quench from the homogenization temperature before aging. Figs. 2 to 5, and Table 11, show the size and shape of precipitate dispersions obtained with the above heat treatments. The heat treatments produce variations in the dispersion both in the grains and along the grain boundaries. Precipitate particles along the grain boundaries are rounded and large (about 1.5 p diameter) in the F5 and F7 structures (Figs. 3 and 5). The grain boundary precipitate was somewhat smaller (0.9 p diameter) in the Q7 structure and no grain boundary precipitate was detected in the Q5 structure using light microscopy. The pre-

Jan 1, 1964

By Jack L. Taylor

Single crystals of tungsten grown from powder -metallurgy swaged rod by high-temperative annealing were deformed in tetzsion at temperatures from 2500 to 5000 OF. Orientation of specittzen tensile axis, strained ratrix, and defortnation bands was determined optically by reflections from {110} etch pits. Slip traces meve analyzed and slip directiorz determined. Results indicate that {110}(111) , {112){111}. and {123}{111} type slip occur in tungsten over the terpe,atuve rutge investigated. Slip is orientation-dependent occuvring on tCuzt cowzbitzation oj slip plane and direction which has the highest critical resolved shear stvess. Overshooting appears to be a general occurrence between 2500' and 5000°F. Dejornatiotz bands show rotation in a directiorz opposite to the yotation of tire tensile axis. DEFORMATION in bcc metals has been reviewed by Maddin and Chen,' Keh and eissman,' and most recently by Nabarro, Basinski, and olt. From these reviews it is apparent that some disagreement exists concerning the crystallography of plastic deformation in bcc metals. There is evidence of noncrystallo-graphic slip, the crystal slipping on or near a noncrys-tallographic plane in the (111) zone for which the resolved shear stress is greatest. There is also evidence to indicate that crystallographic slip occurs in the planes of the same zone. On the other hand, there is agreement that the close-packed direction ( 111) is the slip direction in bcc metals. Further, in pure bcc metals4 and alloys the operative crystallographic slip systems are strongly dependent on temperature. Both crystallographic and noncrystallographic slip have been reportede8 in tungsten, a group VIA bcc metal. The number of slip families which operate in the case of crystallographic slip, however, has been in question. The earliest study by oucher' of single-crystal tungsten tested at temperatures of 1800 to 5000°F led to the conclusion that only {112)( 111) type slip operated. Raymond and eumann recently reached the same conclusion studying deformation by rolling of plasma-flame single crystals at 1800°F; however, only [loo] and [110] orientations were studied. Work at high temperatures by Leber and Pughs on tungsten and Chen and Maddin9 on molybdenum suggests that conjugate slip on nonparallel (110) planes may account for the slip on (112) and (123) planes found by others working with bcc metals. The present paper presents evidence of three families or modes of slip in tungsten in the temperature EXPERIMENTAL PROCEDURE Material. Standard microtensile specimens, 0.160 in. diam by 0.640 in. gage length, were ground from commercial powder-metallurgy swaged tungsten rod, type MK. Specimens were heated for 10 min at 5150°F or 6 hr at 5400°F in vacuum of 1 x 105 Torr or less to produce single crystals. At the lower temperature an average of two out of seven specimens heated in a group developed single crystals throughout the specimen length as shown in Fig. 1, the rest remaining wholly poly crystalline. At the higher temperature, three or four out of seven specimens became single crystal. Other than to note that Laue X-ray photographs generally showed sharp, well-defined spots, no attempt was made to assess crystal perfection or measure dislocation density. Two tungsten single crystals grown from the melt by the plasma-arc process were also used for this study.

Jan 1, 1967

By A. W. H. Morris, E. A. Steigerwald

The jatzgue beizazriov oj Mietal matrix co))zpos~tes in tension -lensiom loading has been imestigated as a junction of Dolume fraclion veinfovcelnent using the model systems of a silver matrix reinforced with contlnuous or dzscontztinuous aligned tungsten jilamenls and continuous aligned steel filamenls. Appreciable impvocetnents in fatigue strength were obseved in all syslems inzvesLigated, the degree of sl renglhenng-increasing with increasing volume fraclion of reinforcement. The mode of fatigue failure was found to be a function of colutrre jp-actiotz and was also noted to be controlled by the relative fatigue and strength characlerislics of the matrix and reinforcemenl. THE advantages to be gained by suitably incorporating high-strength filaments or whiskers into metallic matrices are well-recognized.' To date emphasis has been placed on the experimental determination of tensile strengths and elastic moduli of metal matrix composites measured parallel to unidirectionally aligned filaments. Several attempts have been made to relate experimentally measured tensile properties to theoretical values calculated from the properties of the components on the basis of the relatively simple "rule of mixtures" analysis. However, relatively few data have been reported in the literature on the fatigue behavior and mechanism of fatigue failure of metal matrix composites. In a study of fatigue crack propagation in aluminum plus steel wires and aluminum plus tungsten wires, Forsyth et a1.2 found that the incorporation of small numbers of filaments suitably dispersed were capable of substantially reducing the rate of fatigue crack propagation. For this purpose, the strength of the filaments appeared to be more important than the aspect ratio and the authors reported that parallel filaments were not the most favorable orientation for increased strength. In a basic study of the fiber reinforcement of metals, Williams and 0'brien3 report preliminary results which indicate a considerable improvement in fatigue strength in reversed bending fatigue of a steel wire-reinforced aluminum alloy composite. In a study of the influence of interfacial bonding on fatigue behavior, Baker4 has also reported improved fatigue properties in stainless steel-reinforced aluminum composites. In contrast, Ham and place5 report that, although tensile properties are improved greatly by filament reinforcement, the reinforcement of copper with continuous, brittle tungsten wires up to 23 vol pct was comparatively ineffective against fatigue. The authors attribute the poor fatigue properties of the composite to fatigue hardening of the matrix at the tips of cracks which can build up stress concentrations sufficiently large to fracture proximate filaments. Baker and cratchley6 failed to find marked improvements in the reversed-bending fatigue properties of silica-reinforced aluminum. The study was complicated by the complex behavior in a composite during the compres-sive half-cycles imposed in this type of loading. This was manifested in the failure of the composites by de-lamination, a contributing factor being the presence of aluminum oxide at the matrix-filament interface. Prior to the general acceptance of filament-rein-

Jan 1, 1968

By N. J. Grant, R. Nordheim

An extensive study was made of the aging characteristics of alloys based on the 80 pct Ni-20 pct Cr composition hardened with aluminum and/or titanium, each up to 4 pct. Aging was followed by means of hardness and hot electrical resistance measurements as well as by X-ray and microscopy. Stress rupture tests at 1500°F were utilized as a check on the predicted behavior. THE titanium and aluminum hardened Ni-Cr alloys, exemplified by Nimonic 80 and Inconel X, constitute one of the more important groups of alloys developed to meet the demand for materials retaining their strength at elevated temperatures. For service in the temperature range 1200" to 1500°F, these alloys offer high creep resistance. With increasing service temperature, however, the strength of the simpler Ni-Cr base alloys falls off rapidly so that above 1500°F there is a significant loss of strength. The present investigation was undertaken with the hope that a better understanding of the factors controlling the precipitation hardening of these alloys would make it possible to increase the useful service temperature range. Primarily this investigation involved the study of the effects of titanium and aluminum on the hardening and the subsequent softening at elevated temperatures. The titanium and aluminum contents were each varied between 0 and 4 pct by weight at a constant nickel to chromium weight ratio of about 4:1. (Except when otherwise stated, all compositions are expressed on a weight basis.) The major part of the investigation was confined to alloys with less than 0.06 pct C. Recently several papers dealing with the identity of the microconstituents in the titanium and aluminum hardened Ni-Cr alloys have been published. Using X-ray analysis of the residues from anodic dissolution, Rosenbauml was only able to identify carbides and nitrides in Nimonic 80 and Inconel X. However, since Rosenbaum worked with alloys in the hot rolled rather than in the aged condition, his results are inconclusive. Recently Hignett' reported that the hardening of Nimonic 80 was due to the controlled precipitation of Ni,(TiAl) having the cubic Ni3A1 structure. Taylor and Floydv-" published the results of an investigation of the nickel-rich corner of the Ni-Cr-Ti, Ni-Cr-Al, and Ni-Ti-A1 systems. In the Ni-Ti and the Ni-A1 systems the hexagonal Ni,Ti phase, 7, and the cubic Ni3A1 phase, -y', respectively, exist in equilibrium with the nickel-rich solid solution. The interatomic distances in the basal plane of Ni,Ti and the octahedral planes of the matrix are almost equal, thus explaining the Wid-manstaetten type structure formed when Ni,Ti precipitates from solid solution. When Ni:,Al precipitates from solid solution, it appears usually in globular form, often dispersed along rows corresponding to definite crystallographic directions. The 7 and phases are also the only intermetallic compounds which occur in the nickel ternary alloys with up to 25 pct Cr and 10 pct Ti or Al. Taylor and Floyd found that Ni,Ti takes practically no nickel, chromium, or aluminum into solution. Nial, on the other hand, dissolves a considerable amount of chromium and titanium and some nickel. Up to three out of every five aluminum atoms could be replaced by titanium in Ni,Al. This substitution caused a slight increase (less than 1 pct) in the lattice parameter. With respect to the effect of variation in the titanium and aluminum contents on the high temperature strength of Nimonic 80 type alloys, Pfeil, Allen, and Conway" reported that an 80 pct Ni-20 pct Cr alloy containing 0.20 to 0.30 pct A1 had the highest creep resistance when the titanium content was kept between 1.65 and 2.75 pct. Experimental Procedure The materials used for this investigation were electrolytic nickel, electrolytic or low carbon chromium, sponge titanium and 2s aluminum. The alloys were melted in an indirect carbon arc furnace under

Jan 1, 1955

By L. E. Murr, P. J. Smith

A study has been made by transmission electron microscopy of thin foils of 304 stainless steel fatigued external to the electron microscope in reversed bending, and of thin foils fatigued directly within the microscope in alternating tension. The build-up of stacking faults in the thin foils during fatigue zoas correlated with the dislocatirm structures found in thin films prepared fror fatigued bulk specimens. The performance of the special devices designed for fatigue of thin foils so outlined and the importance of alternative methods of preparation of more uniform fatigue specimens bY vapor deposition are emphasized. INVESTIGATIONS on fatigued bulk aluminum1,' and stainless stee13j4 have revealed the existence of dislocation substructure on examination by transmission electron microscopy of electrolytically thinned foils representative of these bulk specimens. While this technique has proved extremely valuable, it has several shortcomings. First, the method of fatiguing bulk specimens and then thinning to foil for electron-transmission observation allows only one observation of internal structure at any one portion of the fatigue life. Second, thinning the bulk fatigued specimens to foil results in the loss of at least one original surface. Thus, what one sees in the remaining electron-transparent sections is an internal dislocation or fault structure which in many cases cannot be correlated with the original surface markings. This is an undesirable feature, since it is well-known that metal surfaces play an important part in the fatigue process.5 An obvious third undesirable feature of the thinning-from-bulk technique is the fact that static observations have difficulty (in the case of fatigue) explaining the mechanism of a dynamic process. What is required then is a method whereby a selected thin area can be continuously observed either while undergoing cyclic deformation or at various fixed stages of fatigue deformation. While Murr and wilkov6 have reported some success with an apparatus designed to fatigue thin metal foils directly within the electron microscope, the nature of the specimen-mounting procedure and the mechanical features involved in the adaptation of the fatigue device to the electron microscope make this method difficult to operate. It was not possible, for example, to make frequent observations of a selected area because of difficulty in maintaining a chosen area in a stable viewing position inside the electron microscope. Except for the build-up of a dislocation substructure and what are commonly referred to as "slip striations", little else has been reported from observations on thin-foil sections prepared from bulk fatigue specimens. segal17 has found "slip striations" in stainless-steel fatigued specimens which were electropolished from both sides, but gave no explanation as to their origin or identity in terms of lattice imperfections. The research to be reported in this paper was undertaken with the following objectives in mind. First, an attempt was made to devise a technique or techniques whereby thin metal foils could be fatigued and repeatedly observed by transmission electron microscopy. Second, it was hoped that some correlation could be made between deformation striations found in fatigued thin transmission specimens and thin foils prepared from bulk fatigued specimens. These investigations illustrate quite convincingly that a feasible method is available for the direct study of the fatigue mechanism and similar dynamic phenomena in thin transmission specimens inside the electron microscope. I) EXPERIMENTAL METHODS Three modes of specimen fatigue and observation of fatigue damage were used. These involved fatigue of thin-foil specimens in a special arrangement external to the electron microscope and observation of a selected area at various stages in the fatigue life, the fatigue of thin-foil transmission specimens inside the electron microscope, and the fatigue of bulk specimens external to the electron microscope followed by thin-foil preparation for direct observation at predetermined stages. Design of the External Fatigue Clip and Specimen Holder for the Hitachi H.U.11 Electron Micro-scope. The purpose of the fatigue clip was to provide a reversed bending fatigue stress to a thin-foil transmission specimen outside the electron microscope. In order to accomplish this, a flat-bottomed, U-shaped brass clip was made as shown

Jan 1, 1965

By AIME AIME

REGISTRATION and licensing of engineers is now being given consideration by a special committee of the Institute, authorized at the March meeting of the Board of Directors. The subject is one that has recently been or is now actively before engineering organizations in many of the States of the Union. In Washington, D. C., the Washington Society of Engineers and the local sections of ten national engineering societies, including the A.I.M.E., recently had a joint committee investigate the subject: this committee formulating a proposed law that has been presented to Washington engineers for their consideration. At the same time, the committee has summarized the reasons for and against registration of engineers in Washington, D. C. As many of these reasons are of more than local application, they are here reprinted so that all members of the A.I.M.E. may be informed on the subject. It is expected that some report of the Institute's Committee on Registration, State Councils and Professional Development will he made at some forthcoming meeting of the Board of Directors.

Jan 1, 1932

By P. K. Koh

With identical annealing heal treatment the development of major annealed texture component seems to depend primarily upon the degree of cold reduction. Cube texture was evident on annealing- 1/2-, 1,/4- , and 1/8-mil tapes at 760°C, but it dissap-)eared on 927°C annealing of 1/8-mil tape cold reduced 96.9 pct. Some cube texturee remained as tile strongest 927 °C annealed texture component in 1/4- and 1/2-mil tapes cold reduced 93.8 and 87.5 pet, respectively. The switching coefficient increases and the squareness ratio of the hysteresis loop decreases proportionally with increasing cube pole concentration. PREVIOUS studies 1,2 on the 1/8-mil ultra-thin molybdenum permalloy tape established cold rolled and annealed textures and their magnetic performance for switch-core and coincident-current memory applications, The major cold-rolled texture was found to be of {110}<335> which is quite similar to the cold-rolled texture of silver and 70-30 cartridge brass. The major annealed texture components were found to be of {120)-- <001> and {113)<785>. Although the direction for easy magnetization for this type of alloy by the single-crystal technique is not avaliable, knowledge from related studies indicated [Ill] as the easy magnetization direction, similar to that of nickel.&apos; Therefore, a cube orientation, if present in the tape core, would be most detrimental to its magnetic performance.3 In its cold-rolled state the tape had < 111 > directions in the rolling plane 14.5 deg from the rolling direction.&apos; But the coercive force of the tape in such condition will be excessive due to large amounts of internal stresses, and therefore makes its use impossible for memory applications due to long switching time. In lower nickel alloys, suchas 50-50 nickel-iron and 65 pct Ni-Fe sheets, previous investigators4"7 found the presence of cube texture on annealing at 900° to 1000°C. Although no cube texture was found in annealed 1/8-mil tape,"&apos; its presence in some annealed 1,/4-mil tape cores was firmly established a year ago as verified by significant differences in magnetic properties. The present investigation is devoted to the orientation study and related magnetic measurements on three thicknesses of the ultra-thin tape, namely, 1/8 mil, 1/4 mil, and 1/2 mil, cold rolled directly from annealed 4-mil stock in the cold-rolled state as well as after they were annealed at 760°C (1400° F) and 927°C (1700°F). The results obtained might serve to elucidate the development of annealed texture as well as to establish clearly the importance of preferred orientation on the magnetic performance of such memory tape core despite its well-known low magnetic anisotropy exchange energy. EXPERIMENTAL PROCEDURE Samples were taken from one production heat (0.010 wt pct C, 0.004 P. 0.016 S, 0.80 Mn. 0.29 Si. 79.69 Ni. 4.42 Mo. 0.054 Co, 0.002 Ti, 0.12 Al, 0.04 Mg, 14.56 Fe). Annealed 4-mil sheets were cold re-

Jan 1, 1962

By A. J. Garnier, N. H. van Lingen

Rock downhole is known to be lesc. drillable than when brought to the surface. This must be ascribed mainly to the presence under downhole conditions of a pressure differential across already made chips, which hinders their being lifted. The pressure differential has partly a static and partly a dynamic origin. Balling-up of bits is another consequence of this pressure differerztial. Reduction in penetration rate owing to an increase in the strength of the rock is governed by the difference between the mud pressure and the pressure of the for/nation pore liquid. Rotationally symmetric geostatic stresses have 170 effect on drillability. Fracture of rock when drilling will be brille in most cases. The above is supported by laboratory drilling experiments with drag bill and roller bits an elevated mud, pore, and confining pressures On rocks differing in strength and permeability. INTRODUCTION In oil well drilling drillability of rock is found to decrease with increasing depth of the hole. Naturally deep rock will be more compacted and, therefore, harder to drill than shallow rock of the same type. However, apart from this the drillability of a sample of deep and compacted rock brought to the surface is generally much higher than in its original location downhole. In view of the economic implications of this reduction in drillability, it seems worthwhile to analyze its causes. The origin clearly has to be sought in the difference of environment. The only conceivable factors would seem to be the presence of mud under pressure, the pressure of the formation pore liquid, and the overburden of the rock. Down the borehole the rock is compressed triaxially by mud pressure and overburden. It is well known that the strength of rock is increased when confined by external pressure1. Various authors have, therefore, ascribed the difference in drillability mainly to the strengthening of rock by triaxial compression. Another factor, mentioned by Bobo and Hoch5, is that forces. including "pressure differential forces", tend to hold a dislodged particle in place. However, the conditions determining their magnitude are not clarified nor is their effect on drilling rate assessed. In the laboratory, drilling experiments on pressurized samples of rock yielded evidence that pressure differential forces holding the chips down are the major factor in reducing rate at depth. This paper describes the experiments and shows how the results enable both a qualitative and a quantitative interpretation of the factors determining the effect of chip hold-down on drilling rate. The implication with respect to balling-up and jet action is also discussed. The greatcr part of the experiments were performed in the pressure vessel shown in Fig. 1. The spacc between the sample of rock and the vesscl is divided by "0" rings into three separate chambers. The rock sample is confined laterally by pressurized oil in thc middle chamber. Penetration of oil into the sample is prevented by partly jacketing it with brass foil. Thc pressure of the drilling fluid in the hole can be adjusted via the upper chamber. Permeable rock specimens arc water saturated before being drilled. With a properly plastering mud as drilling fluid the pressure of the pore water can be adjusted independently via the lower chamber.

By D. H. Polonis, Gary A. Dreyer

This investigation involved a study of the reactions occurring during aging of supersaturated a phase in a CIL-Si alloy. The aging processes at temperatures below 552°C were studied by means of metallography, microhardness, and electrical resistivity measurements. During the initial stage of aging in the temperature range 275o to 525oC an anisotropic phase, which is visible in the form of striations in the micro-structure formed prior to the appearance of the -phase. This transition phase has been designated k&apos; due to its structural similarity to the k phase. The rate of K&apos; formation during aging increased with aging temperature. At 450o and 525°C the reaction appeared to reach completion before significant amounts of precipitation were observed. The overall precipitation reaction in this system involved four stages: formation of formation of at a grain boundaries, growth of particles in 7-egions, and coagulation of into large particles. The relative role of each of these processes is dependent on the temperature of aging. The formation of phase from supersaturated a during aging increases the electrical resistivity and slightly increases the hardness of a 4.9 pct silicon alloy. The formation of during aging decreases the electrical resistivity and increases the hardness until coalescence of particles begins during the final stages of aging. The coalescence of results in a decrease of both electvical resistivity and hardness. THE available literature does not record a detailed analysis of the aging processes in Cu-Si alloys. Such an analysis has been difficult due to both the limited data available and misleading microstructural observations which have been reported. Previous work suggests that a rather complicated series of processes may be involved in the aging of supersaturated a. The present investigation is concerned with an analysis of the sequence of these aging processes in a 4.9 pct Si alloy. The currently accepted version of the Cu-Si equilibrium diagram, Fig. 1, was published by C. S. Smith in 1940.&apos; This diagram shows a eutectoid at 5.2 pct Si with the high temperature phase, having its composition range entirely to the right of this value. By quenching alloys in the composition range 4.6 to 5.2 pct Si from the region, Smith was able to retain the phase. However, this phase exhibited a striated microstructure which was anisotropic to polarized light. These striations were suggested by Smith to be duplex twins. Using an oscillating crystal X-ray method Barrett2 studied alloys containing 4.0 to 5.4 pct Si quenched from the and regions. The striations observed in quenched specimens were attributed by Barrett to quenching stresses. He found that striations could also be formed by deformation after quenching and identified them as stacking faults in alloys containing 4.0 to 5.0 pct Si. Barrett related the striations in alloys containing 5.0 to 5.4 pct Si both to stacking faults and to a metastable phase which he called The striated structure reported by smith&apos; was also obtained by Hoffmann, et al. 3 By deeply etching their specimens the anisotropic phase on the surface was removed, leaving a structure which was microscopically similar to pure copper. By means of X-ray analysis before and after deformation at room temperature it was concluded that the anisotropic phase was metastable This conclusion has been questioned by Barrett who attributes the discrepancy to superposition of k and lines on the powder patterns of Hoffmann, et alm3 The decomposition of supersaturated according to smith&apos; and Anderson,4 is very sluggish. However, Nony and Dreyer,5 and Hoffmann, et al.&apos; found that deformation increases the rate of decomposition. X-ray studies by Hoffmann, et al on

Jan 1, 1962