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By Zden[e]k P. Bažant

Due to their heterogeneity, most rocks fracture with a zone of distributed cracking ahead of the fracture front. This makes linear elastic fracture mechanics inapplicable. The present study describes a mathematical model in which the progressive microcracking is taken into account by strain-softening stress-strain relation. In a simpler version of the model, the triaxial strain-softening stress- strain relation is obtained by direct adjustment of the elements of the compliance matrix. This formulation is rigorous only if the principal stress directions do not rotate during fracture formation within the fracture process zone. As a more sophisticated and generally applicable model, the so-called microplane model which is an analogue of the slip theory of plasticity is outlined. Comparison with fracture data for various rocks are given.

Jan 1, 1984

By G. W. R. Kuzyk, John D. Smith

Tantalum Mining Corporation of Canada Limited has been mining tantalum ore from the Bernic Lake pegmatite dyke since 1968. The shallow nature of the dyke and relatively high strengths of the various rock types led to the choice of a room and pillar mining method. Rock mechanic studies have indicated that the original pillar dimensions of 50 feet x 50 feet are conservative for existing rooms. Therefore, a plan to reduce the size of pillars using rock mechanics instrumentation to monitor the resulting stress on pillar remnants and stope backs was devised. The paper describes the test work done on the rock types within the pegmatite dyke. The use of Irad stress cells and extensometers in monitoring the stress in pillars is described. The actual results of the program to date are presented.

Jan 1, 1983

By Michael M. Maier, Charles B. Brumleve

The Henderson mine uses the panel caving method to extract molybdenum ore from a deep ore body in an igneous intrusive. Research into caving mechanics and its related problems has yielded fundamental relationships concerning the response of a stressed rock mass to the caving method. The relationships studied through a variety of programs include the following: the evaluation of time and distance related stress fields; the monitoring of the deformation of underground openings and the design implications; ground and mining sequence classifications compared to past support requirements; the response of finite rock masses to zones of high stress concentrations; the evaluation of the subsidence induced by caving; and the microseismic monitoring of cave growth. The cumulative objective of this research is to better understand, predict, and control rock mass response.

Jan 1, 1981

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By F. J. Radd, R. L. McGlasson

The mechanisms of corrosion and corrosion fatigue damages to sucker rods are examined from a fundamental electrochemical viewpoint, and the relationships of sucker rod microstructures to these damaging effects are defined. The common corrosive agents in crude oil production and storage are discussed as to types of attacks that they cause. The variations of fatigue strength with alloy content, surface preparation, and stress ranges are analyzed. Finally, conclusions are drawn as to how microstructures largely influence and control sucker rod performance. INTRODUCTION Greater than 90 per cent of the crude oil produced by artificial lift methods is produced through sucker rod pumping systems. In the USA each year more than $14 million is spent for sucker rods in new and old pumping installations. It is important to make this investment a wise one. Essentially, the sucker rod system is a long series of steel rods, operating under alternating stress loadings and under mechanical vibrations, which connect the surface power source with the subsurface pump. These rods often operate in a variety of corrosive media, including water, brines, carbon dioxide, hydrogen sul-fide, and air. Basically, this paper is concerned with the problem of the behavior of certain steels in various corrosive media under high and dynamic stress patterns. The main objective of this paper is to show how, once the stress effects and the corrosive environments are defined, one can still realize structural control and beneficial influence upon corrosion and corrosion fatigue. FUNDAMENTAL DEFINITIONS AND ANALYSIS In the corrosion and stress behavior of this solid state mixture of iron and iron carbide called steel, one must analyze upon what major factors does its service life depend and of what, exactly, is steel composed. The former question can be referred to two external factors and two internal factors. The two major external factors are: 1. the nature of the stress patterns — size and range of stresses present 2. the nature of the corrosion — erosion environment — the corrodent and/or wear involved The two fundamental internal factors that govern the strength and useful life of a steel both in normal duty and in heavy-duty corrosion service are: 1. the nature of the steel volume properties 2. the nature of the steel surface properties For the latter question normal steel is defined as a solid mixture of iron and iron carbide particles, generally with certain accidental and intentional elements present. (The amount of iron carbide present is determined by the carbon content of the steel.) These additional elements generally dissolve into either the iron (ferrite) or the iron carbide (cementite) components.

Jan 1, 1955

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By J. L. Swedlow, M. L. Williams

Two standard techniques for assessing fracture initiatlon in sheet specimens involve measurements of 1) the applied load of fracture which, via linear fuacture mechanics, is used to find the fracture tough/less SC (or SIC), and 2) the velative displacement of fracture of the opposite free faces of the crack (COD). In the past, the quantitative association between these two parameters has not been determined in detail, owing to the mathematical difficulties of computing. the stress and strain fields in the combined elasto-plastic flow near the crack. Using a numerical technique Irecently developed and applied to a 7075- TO' aluminum plane stress specimern, the two parameters noted have been determined and associated quantitatirely. CONSIDERABLE effort has been expended in selecting a rigorous yet practical manner for predicting fracture. The usual point of departure is the modified Griffith criterion in which the mechanism of energy dissipation is reflected in Sc (or SIC), the parameter of "fracture toughness". Sc. differs from the surface energy used by Griffith in perfectly brittle fracture in that it includes the effect of plastic flow in the vicinity of the crack tip. Because plastic flow alters the stresses and displacements predicted from the usual linear theory of fracture mechanics, and because analysis of the nonlinear stress-strain field has presented great obstacles: only estimates of several pertinent quantities have heretofore been available. Nevertheless, two parameters have often been measured experimentally althougll usually just at the point of fracture. These are the energy release rate, or fracture toughness 9, (or I,), and the crack-opening displacement (COD). Such observations have been used in connection with frarture criteria and have been most helpful in design, although their application requires care with respect to changes in geometrical configuration from that upon which the criteria were based 1,2 Recently, however, a reasonably accurate and comprehensive method for analyzing the elasto-plastic flow has been devised and applied to plane stress specimens having arbitrary octahedral stress-strain curves.3 It thus becomes feasible to compute, albeit numerically, both the fracture toughness and crack opening as functions of the applied tensile loading on a typical specimen geometry. As a result, it is now possible to associate these two parameters quantitatively, and thereby to associate data obtained by one method with data pertaining to the other. ELASTIC ANALYSIS For the case of linear elasticity, it is relatively easy to deduce the connection between various measures of crack deformation. Using, for example, the singularity analysis, it is found that the leading term of the Airy stress function x f°r symmetrically applied loadings on an isotropic medium is

Jan 1, 1968

By Y. L. Su, R. Stefanko, Y. J. Wang

This chapter describes a new approach to the solution of stress distribution around underground openings utilizing the finite element method and employing stochastically simulated rock properties. It is well-known from extensive laboratory tests that the properties of rocks, e.g., Young's modulus and Poisson's ratio, are not single-valued but form some distribution. If the scatter of test data is attributed to the variability of the rock itself rather than due to an inadequacy in test procedure, then stress solutions have to consider these variations. Utilizing this basic philosophy, the present study was initiated. A long circular opening subjected to plane strain in a hydrostatic stress field was chosen as a specific example to illustrate this approach. The technique adopted in solving stress distributions was based on the finite element method. This method is essentially a generalization of standard structural analysis procedures in which the continuum is idealized as an assemblage of "elements," interconnected at a finite number of nodal points. It is capable therefore of handling different material properties for individual elements in the model, if desired. In this study, each individual element was assumed to be isotropic, homogeneous, and elastic. However, values for Young's modulus and Poisson's ratio were randomly varied from element to element according to an assumed frequency distribution.

Jan 1, 1970

By Peter L. Raffo, Walter R. Witzke

RHENIUM has a melting point of 5750°F, the second highest value among the metals.1 Its refractory nature should thus make it a useful material at high temperatures. The only available data on the high-temperature properties of bulk rhenium are from the work of Flagella and Tarr.2 These authors have shown that, over a wide range of temperatures and stresses, no appreciable linearity exists in a log-log plot of the minimum creep rate or rupture life vs stress. The purpose of the present letter is to describe some exploratory experiments designed to study the creep rate-stress-temperature relation and other facets of the creep of rhenium. The tests were carried out in vacuum in the temperature range 2200" to 4000°F (0.43 to 0.72 Tm,) at stresses ranging from 4 to 20 ksi. The powder metallurgy rhenium was purchased as 0.04-in.-thick sheet. The sheet is nominally 99.97 pct pure with the major impurities being iron (70 ppm) and molybdenum (25 ppm). The sheet was machined into specimens having a 1-in. gage length and a 0.25-in. gage width. The specimens were preannealed in hydrogen at 3000°F for 1 hr. This treatment produced

Jan 1, 1970

By R. E. Rowlands, I. M. Daniel

An experimental study is discussed of the state of strain, deformation and fracture around lined and unlined cylindrical cavities in rock under biaxial compressive static loading. The specimens were limestone plates 36 in. high, 24 in. wide and 3 in. thick with a 4 in. diameter hole unlined or lined with hydrostone and aluminum liners. The ratio of horizontal to vertical applied stress was one-third. Experimental techniques used were strain gages, differential transformers and photoelastic coatings. Strain distributions were plotted along the horizontal axis of symmetry for various levels of applied stress. The agreement with theory was good at low stress levels but appreciable deviations occurred at higher levels and near the hole. The experimental strain concentration factor was nearly the same, slightly higher and appreciably higher than the theoretical value for the hydrostone-lined, unlined and aluminum-lined specimens, respectively. Failure modes were splitting along a vertical plane for the unlined and hydrostone-fined specimens, compressive (shear) failure for one unlined specimen and splitting with radial cracking for the aluminum-lined specimen. In the latter, a maximum tensile stress of more than three times the uniaxial tensile strength existed at the interface with the liner at the time of fracture,

Jan 1, 1971

By J. V. Vogel

Jan 1, 1969

By R. A., Pallanch

THOUGH the flotation of gold ores has come into the lime- light largely in recent years, it is not a product of recent economic conditions but rather as old as flotation itself. It could hardly be other- wise, since gold, when in the right state of comminution and surface condition, is one of the more readily floated of minerals. In early practice it was not generally recognized that gold was floated as well; it was - thought that the gold was bound up with sulphide minerals that floated, but now we know that free gold must have been floated as well.

Jan 1, 1935

By AIME AIME

T HE Mining Methods Committee held its initial meeting* on Tuesday afternoon, with F. W. Bradley in the chair and W. Y. Westervelt as vice- chairman. The first paper to be presented was "A Plea for a U. S. Court of Patent Appeals," for which Kenneth W. Greenawalt ably pleaded. The paper (which was published in full in last month's issue) is so carefully prepared that no synopsis can do it justice. It discusses the opposed views of some patent lawyers and other lawyers and members of the judiciary as, for example, Chief Justice Taft who is quoted as saying in 1921: "I think it is a great deal better to take a first class lawyer and a first-class judge and make him a good patent expert than it is to take a patent expert and try to make him a first-class lawyer and a good judge." Mr. Greenawalt argued the need for specialized scientific and engineering interest and understanding to enable a lawyer or judge to prepare or interpret patent specifications and decide the originality necessary for a valid invention. He proposed the special U. S. Court of Patent Appeals to also counteract the costly confusion and injustice now ruling where a patent may be declared valid in the courts of certain States and invalid by the courts of other States.

Jan 1, 1930

By Robert D. Longyear

IN MOST diamond core drilling the primary objective is the recovery of samples to be used for chemical analysis, physical tests, or visual inspection. Unless these samples are reliable and the information systematically recorded, the time and money spent in securing them are largely wasted. A properly taken diamond-drill sample is similar to a properly moiled channel sample but more accurate. No channel sample can be moiled in as even a groove as the smooth cylinder of material normally removed in diamond drilling. More important still, sampling by the diamond drill practically eliminates that personal equation which Jora1emon4 reference numbers apply to publications listed in the bibliography at the end of this article) has aptly termed "the almost magnetic attraction of the most conscientious hand toward rich pieces of ore."

Jan 1, 1937

By W. F. Wheeler

IN the study of the coals of Illinois now being carried on by the State Geological Survey, an attempt is being made to determine the most satisfactory basis of comparison between different coals. The following discussion is based upon work done for the survey in the laboratories of the State University and under the general direction of Prof. S. W. Parr. " Pure coal " has been defined by Mr. A. Bement1 as ash- and moisture-free coal, and the use of this " pure coal " as a basis for comparing different bituminous coals has lately been much discussed among engineers in the middle West. By some the B.t.u. of the pure coal is being used to check calorimetric results, and to calculate the calorific value of different coal-samples from the same seam, for which purposes it is necessary to assume-first, that the composition and calorific value of pure coal from different parts of the same coal-seam are uniform, and, second, that these values remain constant after the coal is mined, both of which assumptions there are reasons to believe are inconsistent with the facts. Certain variables are included in pure coal, as ordinarily defined, and disregard of them may lead to serious error. In any event, where delicate shades of difference are involved, no sure interpretation of results can be made, unless these variables be eliminated. As a basis of comparison between coals, ash- and moisture-free coal is much to be preferred to " dry coal," and still more is it to be preferred to " moist coal," as ordinarily reported in analyses. There are, however, two constituents other than ash and moisture which are similar in effect to them, and which

Jan 1, 1908

Secretary's Note.—M. Beutter's introductory remarks, being simply a resume of Prof. Hone's paper, with a disclaimer of the intention to criticise it, have been omitted, and the remainder of this contribution lias been somewhat condensed, without omitting any essential statements. M. Beutter, St. Etienne, France* (communication to the Secretary†):—Professor Home observes in $ 47 of his paper that the fluid-compression of steel diminishes piping by forcing the liquid and viscous metal, while the pipe is forming, or after it has formed, into the space so produced, and proceeds to study the different systems of compression, alluding to the four principal ones: Whitworth, Illingmorth, Williams, and Harmet. Having now for many years had in use the last-named process, that of M. Henri Harmet, I shall attempt to explain the difference between it and the three other processes named. The Harmet process does not diminish or close the pipe after it has formed, but prevents it from forming; and I may add that it is the only one of the four which produces this result. It is true that the Whitworth process diminishes the interior hollow by localizing it around the central axis of the ingot, which is afterwards removed by trepanning the hollow forg-ings for which this process has been, I believe, always exclusively used. The Illingworth and Williams processes, which, in my opinion, are applicable only to small ingots, of necessity allow the pipe to form, or (to use the expression of Professor Howe) they allow the surface of the lake of liquid steel to sink into the interior of the ingot, since they involve waiting a certain time before compression, so that (in the case of the Williams process) the ingot-mold can be opened without danger, or (in the case of the Illingworth process) so as to avoid the risk that the steel may enter the grooves produced by the removal of the distance-bars. During the time required for

Jan 1, 1908

By Richard S. Culver

In spite of the widespread interest in rock bolt research, relatively little is known about the critical region surrounding the bolt anchor. In analyzing the stress distribution around an opening resulting from rock bolt support, it is commonly assumed that the bolt is fixed at a point far enough from the surface so that the anchor does not influence the performance of the bolt. Furthermore, a bolt anchor is assumed to per- form satisfactorily if it will hold the design load with a minimum amount of load relaxation, commonly called bleedoff. From the standpoint of the design engineer both of these assumptions are reasonable, but they ignore the fact that the extremely high stresses in the region of the anchor are capable of generating fractures in the rock. Lang1 estimated the bearing stresses for a slot and wedge anchor on a one-inch-diameter bolt to be as high as 125,000 psi. This paper describes a more thorough analysis of the magnitude of the stresses around the anchor and the nature of the potential fractures that might result. It should be emphasized that there are two types of anchor-associated fracturing which may occur. The more common form, particularly in soft rock, is severe localized crushing of the rock in the immediate vicinity of the anchor, which makes securing the anchor difficult and causes bleed- off. It is also possible to develop larger single fractures which propagate out from the anchor, affecting the strength of the entire rock mass. The formation of these larger fractures is of primary concern in this paper. In addition to estimating the contact stresses and pullout load for slot and wedge bolt anchors, Lang carried out an important study of rock bolt interaction which served as a basis for the experimental phase of this investigation. In the first phase of his tests, a plate of photoelastic plastic was compressed by a row of piano wire bolts, simulating the interaction of bolt stress fields to form a zone of uniform compression (Fig 1). To show the supporting effect of this beam, hr carried out another test series

Jan 1, 1968

By M. Gensamer

IN applied mechanics and in metallurgy the transition from elastic to inelastic action is a matter of considerable interest and importance. Often the first inelastic deformation is apparently quite homogeneous; that is, uniformly distributed throughout the specimen. Sometimes this deformation is heterogeneous; that is, localized; inelastic deformation proceeds to some definite amount in restricted regions before adjacent regions of the specimen are inelastically deformed. In such cases the deformation does not become homogeneous until the whole specimen has been deformed the amount corresponding to that for each localized deformation. If the test is stopped before uniform extension sets in, the heterogeneous character of the deformation is apparent on the surface of the specimen through characteristic markings, which have been called "Lüders"' lines, "Hartmann's" lines, the "Piobert effect," or simply "flow figures." These markings are the source of considerable trouble in fabricating operations, particularly in the deep drawing of steel sheet. In many cases where the transition is of this nature, the stress developed at the upper limit of the elastic range is greater than the stress during the period of heterogeneous deformation, giving rise to the familiar "drop of the beam" effect in testing. The amount of the yield-point elongation, as well as the value of the stress at the lower yield point (the value to which the stress drops when yielding begins), are functions of the temperature and the testing speed. Lower temperatures and faster rates of testing increase both the yield-point elongation and the yield-point stress. These matters have been ably discussed in a recent paper by Winlock and Leiter1 though, as brought out by the discussion of that paper, the phenomena are but little understood. The purpose of the present paper is to clarify the problem through the application of a simple principle, and to show that, through the application of this principle, a number of phenomena in the plastic deformation of metals become more readily understood. The principle is this: During homogeneous flow, the rate of work-hardening is greater than the rate of change of stress resulting from change

Jan 1, 1938

By R. Rocca, M. B. Bever

THE adiabatic elastic deformation of a body is accompanied by a change in temperature. This phenomenon is known as the thermoelastic effect. Under adiabatic conditions the temperature of a metal bar is decreased by an elastic elongation and is increased by an elastic compression. All materials which elongate on heating behave in this manner. The sign of the thermoelastic temperature change is reversed for the few materials which have a negative coefficient of thermal expansion. The following equation for the thermoelastic effect can be derived from fundamental thermody-namic theorems, as shown in the Appendix: dT8 =-a1/cs T dss [1] Cs In this equation, T is the absolute temperature, S is the entropy, a, is the coefficient of linear thermal expansion, cs' is the heat capacity per unit volume at constant stress and s is the stress (positive in tension). Eq 1 can be applied to small, but finite changes in stress in the following form: ?Ts =- a1/cs T?ss [2] The sign of the temperature change AT is opposite to that of the change in stress s for materials which have a positive coefficient of thermal expansion. Eq 2 has been verified for many different materials and stresses at room temperature. No previous publication appears to have been devoted to an in- vestigation of the thermoelastic effect over a range of temperatures. Review of Literature Lord Kelvin (W. Thomson) presented a general theory of the thermoelastic effect in 1851' and later applied it to a solid, subject to an arbitrary system of stresses'. His analysis was based on a cycle of isothermal and constant-strain transformations and led to Eq 2 above. Even today, one of the clearest expositions of the thermoelastic effect is found in Lord Kelvin's article on elasticity in the Ninth Edition of the Encyclopedia Britannica (1878). R. ROCCA, Junior Member, and M. B. BEVER, Member AIME, are Research Assistant in Metallurgy and Associate Professor of Metallurgy, respectiuely, Massachusetts Institute of Technology, Cambridge, Mass. AIME New York Meeting, Feb. 1950. TP 2760 E. Discussion (2 copies) may be sent to Transactions AIME before APT. 1, 1950, and is scheduled for publication Nov. 1950. Manuscript received Oct. 15, 1949.

Jan 1, 1951