Search Documents

By H. F. Silliman, Daniel R. Hull, John R. Freeman

IN the normal operation of a brass-rolling mill, sheet and strip has, for the most part, been finished in comparatively thin gauges, involving a substantial amount of coldwork and a considerable number of anneals. This condition has been disturbed by the prep0nderance of cartridge brass, which is not rolled to thin gauges, and particularly by brass for artillery cartridge cases, on which the mill may finish its work at a thickness between 0.400 and 0.900 in. Obviously, the amount of rolling and the number of anneals to which such a product can be subjected are small compared with strip that is carried to a thickness of a few hundredths of an inch. As a result, critical examination into the internal condition of metal has been made on an extensive scale at a stage of manufacture that would not, in normal times, have been chosen for complete inspection. Under these conditions, a type of defect has been recognized that is not seen at thinner gauges. It might be more accurate to call it the appearance of a defect, since it refers to an apparently laminated, discontinuous structure, which, in fact, does not exist as such, and disappears after suitable treatment. For this reason it has been called a phantom lamination, which the authors consider an appropriate term. It is the purpose of this paper to describe the phenomenon and the conditions of its occurrence and, at least tentatively, to discuss its nature and cause. Great numbers of phantoms may be found in 2: 1 brass, either hot-rolled or cold-rolled. They are also found in 70-30 brass, sometimes when hot-rolled and generally when cold-rolled. It is not believed that phantoms are confined to these alloys but this paper is limited to them for the purpose of description. HOT-ROLLED 2:I BRASS For illustration, therefore, a typical cake of hot-rolled 2: 1 brass has been chosen. This was rolled to a slab 7/8 in. thick, from a casting 5 in. thick by 24 in. wide by 18 in. high, which was believed to have been sound. After hot-rolling and cooling, the slab was sheared and a portion of such a shear cut is shown in Fig. 1. It would be difficult to convince anyone viewing this specimen that the metal was not unsound. The impression would be confirmed by the appearance of a tensile break, as shown in Fig. 2. This is an ordinary tensile-test piece from metal just described. Although there was nothing in its tensile strength or elongation that suggested unsoundness, it appeared run through with pipes and laminations. To question the reality of such a condition would imply questioning the obvious. But, considering the history of the metal, it w0uld be difficult to believe that it could be so bad as it appeared. It seemed reasonable, though, that if the defects were what they appeared to be, they could be traced back from the sheared or broken face.

Jan 1, 1945

By C. W. Volek, J. E. Chappelear

The injection of a hot liquid into initially cool porous media, saturated with the same liquid and surrounded by two impermeable but heat conducting media (cap and base rock), has been studied both experimentally and theoretically. The temperature dependence of the viscosity was included in the theoretical model, but it was assumed that the specilic heats and densities of the various materials were independent of the temperature. Solutions to the theoretical model were approximated by numerical methods. Both theoretical and experimental results indicate that center-line temperatures are significantly higher than boundary temperatures. Comparison of experimental and theoretical results with a cold/hot viscosity ratio 01 19:1 were in reasonable agreement. Theoretical calculations show that the effect of the temperature dependence of viscosity was very significant at ratios of 100:l to 1000:1, which are typical of those that occur when injecting hot water to flood heavy oil reservoirs. INTRODUCTION We consider the problem of prediction of fluid flow and temperature distribution in an initially cold-fluid-filled reservoir on the injection of the same hot liquid by the use of mathematical and physical models. The results reported are for a two-dimensional rectangular section of the reservoir, as shown in Fig. 1. The injection and withdrawal faces are assumed to be equipotentials for fluid flow. The ultimate purpose of such models would be to predict hot-water injection performance. However, we note that in the work presented here, one of the most significant aspects of the problem — the instabilities resulting from two-phase, water and oil flow — is not included. We will not give a historical review, but refer instead to the paper of Spillette and Nielsen,1 which contains a rather complete bibliography and critical discussion. The physical problem is exactly the same as Spillette and Nielsen, except for certain simplifications in our assumptions. The mathematical details are somewhat different, and we will present the details of our method here. The mass flow equation, which is elliptic in character, is handled by successive overrelaxation. The heat flow equation, which is parabolic in character, is handled by a straightforward explicit approximation. Some difficulty arose in the over-all heat balance due to small errors in the solution of the mass flow equation, and we feel that a different formulation of the heat flow equation would be desirable for future work. In addition to the mathematical solutions for the temperature distributions in a porous medium due to the injection of hot liquids, experimental data are presented to check the validity of these solutions. A schematic diagram of the model is shown in Fig. 2. Certain qualitative physical conclusions were obtained from our numerical and experimental results. These are: 1. Assuming high (infinite) conductivity normal to the bedding plane in the reservoir is a poor approximation, and may lead to overestimates of the total heat losses (to cap and base rock) of as much as 50 percent. 2. More heat is retained in the reservoir (per unit of heat injected) for higher viscosity changes. 3. Any particular temperature isotherm moves more rapidly along the center line for higher viscosity changes. Consequently, the approximation of temperature independent viscosity is not suitable for obtaining quantitatively correct results. MATHEMATICAL MODEL Our mathematical model is that of a reservoir of thickness 2h. The problem is idealized from that of a linear hot-water drive, and we imagine that the input face is sufficiently far away from the injection wells that the stream lines enter it normally. Similarly the production wells are far enough from the outflow face that the flow lines leave it normally. The reservoir and surrounding cap and base rock

Jan 1, 1970

The Library of the above-named Societies is open from 9 A.M. to 10 P.M., except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 12, 1917

By J. R. Jargon, H. K. van Poollen

Non-Newtonian fluids may be injected into a reservoir during secondary recovery operations. The non-Newtonian fluid used in this work is a power-law type of fluid that is, the viscosity of the fluid decreases as the flow rate or rate of shear increases. This paper presents equations for steady-state linear and radial flow of such fluids, transient behavior results from a finite difference model of a radial system, and transient behavior results from a field test. The equations that describe the flow of a non-Newtonian fluid are non-linear and are solved numerically. Finite difference solutions are presented as curves of dimensionless pressure drop at the wellbore us dimensionless time for a constant injection rate. Solutions were obtained for 5-percent, 10-percent and 100-percent PV of a non-Newtonian fluid for injection rates of 1, 10, 100 and 1000 cc/sec and for a 5 percent PV of non-Newtonian fluid located at T = Tw' 3, 10, 20, 50 and 100 ft for a flow rate of 1 cc/sec. The buildup curves do not exhibit a stmight-line portion as is the case for Newtonian flow through porous media. Correlations also are shown for the productivity index vs rate for the computer model study and the field tests. INTRODUCTION During various secondary recovery operations non-Newtonian fluids are injected. Such fluids, in general, include thickened water and gelled fluids. The term "non-Newtonian" implies that the viscosity is not only dependent upon temperature and pressure, but also on the rate of shear that is applied to the fluid. For example, water, which is a Newtonian fluid, will have essentially the same viscosity no matter what rate of shear is applied. A pseudo-plastic fluid exhibits a decreasing viscosity when higher rates of shear are applied; a dilated fluid has an increasing viscosity with increasing rates of shear. The objective of studies performed and described in this report is to obtain relationships and mathematical and empirical descriptions of the flow of non-Newtonian fluids through porous media. Simple mathematical relationships, computer studies that include the unsteady-state behavior of such fluids, and field tests are used. PREVIOUS LABORATORY STUDIES Laboratory studies have been performed by several investigators. The fluids used in one investigationl were surfactant-stabilized dispersions of water in hydrocarbons. Its Fig. 6 is reproduced as our Fig. 1. This effective-viscosity vs frontal-velocity diagram shows that this fluid is of the power-law type over a fairly large range of frontal velocities. Gogartyl developed an equation for the effective viscosity as a function of shear rate that reduces to Eq. 2 for frontal velocities greater than about 2 ft/D. The fluid characteristics used in the present study are similar to those reported by Gogarty. Christopher and Middleman2 performed experiments with power-law fluids flowing through pipes packed with glass beads. They used a modified Blake-Koteny

Jan 1, 1970

The Library of the above-named. Societies is open from 9 A. M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 5, 1918

The Library of the above-named Societies is open from 9 A. M. to 10 P.M., except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information, will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will he sent more promptly and in more usable shape.

Jan 8, 1917

The library of the above-named Societies is open from 9 A.M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 10, 1918

The Library of the above-named Societies is open from 9 A.M. to 10 P.M., except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 11, 1917

Critical Shortage of Engineers M AN POWER commitments for defense, superimposed on normal domestic requirements, exceed the available supply of labor. The armed services, industry, and the professions are sizing themselves up man power-wise and are announcing that serious shortages are imminent or already in existence. The engineering profession is facing serious shortages. The main reason for this is the recall of engineering and scientific personnel to the armed services.

Jan 4, 1951

The Library of the above-named Societies is open from 9 A. M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references, and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 4, 1918

By W. van der Knapp

A theoretical and experimental ana1ysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The result enable one to deduce directly the effect of large increlents in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical rules surface, the generating lines of Which have a slope according to the solid rock compressibility. Analytical expression for such a ,surface is very simple. It follows that the bulk and pore compressihilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be conduded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could he related by means of a simple empirical formula. Results from the described study find a direct applicxtion in material balance calculations and in prob1ems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equatiorls for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 1.5 to -10 prr cent porosity that laboratory measured porosities may differ from those lender reservoir conditions by about I per cent of their value. The difference for low porosity limestotnes can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to he very small. General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot1, Gassmann2 and Geertsma.2 Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension. It has been known for a long timei that the stress-strain relations of a packing of spheres are essentially noninear. Our experiments show that for almost all reservoir rocks which arc elastically deformable the relation between volume and loading is also a nonlinear one, resembling that of a packing of spheres very closely. The behavior of these media is often described by using the linear stress-strain relations for small incremental stresses and strains in the vicinity of a pre-stressed condition." The present study differs from these considerations in that it enables one to deduce the effect of large increments in the stresses directly. In analogy to the stress tensor for a homogeneous body the stress tensor for a porous body can be written in the conventional way: where the tensor components, o, and t, represent the total forces acting on the faces of a unit cube of porous material. This tensor can be split into two parts. a hydrostatic and a deviatoric part, as follows2,3,1 where the component of the hydrostatic stress system, a. equals The hydrostatic stress causes a change in volume whereas the deviatoric stress system gives rise to a change in shape only. One of the difficulties in describing changes of volume occurring in reservoir rocks is that the relations connecting these volume changes with external and internal stresses are essentially non-linear. A complete description requires the bulk volume, V,,, as well as the pore volume,V,,. to be known as a function of both the changes in pore fluid tension (v) and the hydrostatic tension on the outer boundary.

The library of the above-named Societies is open from 9 A. M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 1, 1919

The library of the above-named Societies is open from 9 A. M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 12, 1918

R. W. Guard (General Electric Co., Schenectady)— The method of fractional replication discussed by the author has proven very valuable to us in applied research connected with alloy and process development where many of the same experimental difficulties exist. Several of our experiences may be of assistance to those who want to apply the method in these fields. Contrary to the author's observation that interactions are rarely significant, we have found in a number of cases that first order interactions exist which are significant and metallurgically important. Because of this difference there are two further precautions which should be taken in order to minimize the difficulties from this point. First, in evaluating the importance of

Jan 1, 1957

The Library of the above-named Societies is open from 9 A.M. to 10 P.M., except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on milling and metallurgical subjects; to determine the existence of mining maps, arid to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 10, 1916

D. C. JACKLING, the father of the porphyry coppers, has been honored for his pioneering in that field. There is another facet to Mr. Jackling's activities, one which now may prove an even greater monument than the big coppers-the story of his venture in taconite beneficiation. The essence of his porphyry development was mass handling of material. Not alone mining on a large scale, which was done on the Mesabi Range at the turn of the century, but the integration on a previously unknown scope of mining, milling, concentration, and in many cases, of final reduction to metal at the site. This was mass production applied to mining, treatment of a very low grade source material, previously considered submarginal.

Jan 1, 1954

By I. F. Jackson, H. L. Hartman

Hard-metal inserts have received considerable attention in the mining industry recently for a variety of excavating and penetrating purposes. Their use in percussive drilling and in coal cutting machines is well known, but attempts to utilize them in cutting materials such as dimension stone have been discouraging because of excessive tool wear and failure. Particular attention is given to those properties of hard-metal inserts that affect their resistance to wear. A consideration of the actual wear mechanism shows the importance of correct mounting of the inserts and of the selection of suitably powered driving motor so as to achieve minimum tool wear and maximum tool life. Comparisons are made between the performances of types of hard-metal inserts, relating their inherent properties with results obtained in laboratory tests. As part of a broad program to improve the quarrying and processing of industrial minerals, The Pennsylvania State University has been investigating the machinability of slate under laboratory and field conditions. It should be emphasized that the results of the research presented in this paper are also applicable to other natural structural materials, and particularly to the more workable ones such as limestone and sandstone. Improvements which accrue in cutting and sawing should prove of benefit to all the dimension stone industry. Further, it may be pointed out that the results reported here are applicable to rotary drilling (with drag bits) as well as to cutting and sawing of rock. INVESTIGATIONS IN RELATED FIELDS The investigation was initiated with an extensive survey of available literature related to metal cutting and to rotary drilling. The following similar features between metal cutting and slate cutting became evident: 1) Hard-metal inserts are widely used as a cutting tool in both cases. 2) The forces acting on the tool may be resolved into normal and tangential components. 3) Rate of penetration and tool wear are important criteria in each case. On the other hand, important differences also exist: 1) Most metals, exhibit plastic behavior, while slate (and most rock) is a brittle material under normal conditions. 2) In metal cutting the component of force acting parallel to the surface of the workpiece is considerably greater than the force holding the tool against the workpiece. 111 slate cutting, this situation is reversed. Similarities between drag-bit rotary drilling and slate cutting are as follows: 1) In both casts, a tool, usually of the hard-metal insert type, is used to penetrate a brittle material. 2) The drilling forces and related variables, such as rotation speed, are similar. 3) Chip formation in each case is essentially the same. 4) The shape of the tool is similar in rotary drilling and slate cutting. Important differences are also apparent: 1) The objective of drilling is to produce a directed hole, while in cutting it is to form a kerf. In core drilling, however, a kerf is also produced. 2) The horizonta1 component of force in rotary drilling decreases from the center to the outside of the tool, whereas in slate cutting the component is almost uniformly distributed across the width of the tool. 3) The power absorbed in the drill rod is greater in rotary drilling. 4) The clogging action of chips, if excessive power is applied to the tool and if flushing is insufficient, is more serious in rotary drilling. Because of the striking similarities between metal cutting and slate cutting, and between rotary drilling and slate cutting, it was considered that the findings of investigators in those fields would serve as a guide for experimental studies of slate cutting. The following is thus devoted to a discussion of those aspects of metal cutting and rotary drilling pertinent to the present investigations.

Jan 1, 1962

By C. A. Heiland

FOR the past three years, the senior writer has carried out, with inter-ruptions, a series of investigations into the characteristics of prospecting seismographs of a wide variety of construction. Early in 1932, a com-plete equipment was developed for both refraction and reflection observa-tions; its first function being, however, the application in reflection shooting. The performance of the equipment proved to be highly satis-factory in a series of field tests' which were carried out by the junior writer, whose services were loaned to the Colorado School of Mines by courtesy of the Plains Exploration Co. in Denver. The various problems that were encountered in the construction of the equipment, in its application in the field, and in the interpretation of the results, are fully treated in Publication 47 of the Department of Geophysics of the Colorado School of Mines. Its first part deals with the various problems encountered in the design of the instruments, and presents a discussion of such topics as the free and forced oscillations of damped and undamped mechanical seismographs, the action of oscil-lographic recording instruments and amplifiers, the characteristics of electromagnetic seismographs, and the requirements of damping, natural frequencies and static magnification for the pickups, amplifiers and oscillographs used in refraction and reflection seismographs. Further-more, a detailed discussion of the various methods of static and dynamic tests of seismic receivers, and a description of the reflection equipment developed at the School of Mines is presented. Unfortunately, a delay has occurred in the publication of the first part of this investigation concerning the instrument problems. There-fore, the second part, dealing with the field problems, is herewith pre-sented first.

Jan 1, 1933

By John T. Norton, Matthew J. Donachie

Residual lattice strai?zs were produced in 2024 aluminum and ingot iron by uniaxial tensile deformation. These strains were rneasured on the original surface and ulith depth below the surface. The strains conformed approximately to those from a macroscopic stress distribution but they were not truly macroscopic in nature. The exact mechanism which apparently causes the coherently difi9,acting region of each grain to behave as if macroscopically stressed was not determined. MACROSCOPIC stresses in metals produce strains in the lattice which result in X-ray line broadening and line displacements. The latter effect can be utilized in a technique for determining stresses in metals as first shown by Lester and born.' Subsequent advances in technique have enabled the X-ray method of stress measurement to be satisfactorily applied to many problems involving residual stresses of a macroscopic nature, such as those due to welding, grinding, shot-peening, and so forth. In the case of stresses such as those described above, the correlation of X-ray- and mechanically determined data has been generally good. However, plastically extended polycrystalline metals have sometimes been reported2 to show line displacements upon release of the applied tensile load, yet the nature or origin of the residual lattice strains, rls, producing these displacements has never been clear. As will be pointed out, this lack of clarity regarding the macroscopic or microscopic nature and origin of these stresses casts doubt on the validity of results achieved by the commonly accepted techniques of X-ray stress measurement. This anomalous behavior requires clarification to remove the doubts concerning X-ray stress measurement. The present paper is the result of an investigation of the interesting behavior of such plastically extended polycrystalline metal bodies. The studies were originated to carry out the following tasks: 1) Observe whether a residual lattice strain is produced as a result of plastic extension and show whether any residual lattice strains produced can be related to the usual concept of a macrostress. 2) Examine the origin of any residual lattice strains observed. 3) Consider the implications or consequences of the existence of such residual lattice strains on the problem of X-ray stress measurement. THEORY 1) Lattice Strains. The theoretical developments necessary for the treatment of lattice strains and their relation to stresses follow from the classical theory of elasticity and have been adequately covered by arrett. For an isotropic solid under homogeneous deformation, it can be shown that, for uniaxial stresses where Dl is the macrostress acting in the longitudinal direction; E$L is the lattice strain in the plane defined by the surface normal and the longitudinal direction at an angle, , from the surface normal; ET is the similar strain in the transverse plane; E is Young's modulus; and v is Poisson's ratio. Eq. [2] is independent of angle + and Eq. [I] is a linear function of sin2, see Fig. 1, and can be solved analytically for DL if E and u are known and EL is measured. Thus, a uniaxial macrostress will be indicated by a linear E,L vs sinZ plot and a

Jan 1, 1962

Jan 1, 1914