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By C. R. Johnson, R. A. Greenkorn, E. G. Woods

A new method of reservoir evaluation called pulse-testins has been developed for describing formation properties between wells. Pulse-testing utilizes a sensitive differential-pressure gauge at a responding well to measure and record the response generated by a series of flow rate changes (pulses) at an adjacent or pulsing well. Since the pulse-test instruments have a sensitivity of about 0.001 psi, pulses of several hours or less in duration will generate a measurable response in most reservoirs. For this reason, many well pairs can be tested in a short period of time with little interference in field operations. Comparison of pulse-test results to conventional testing methods shows that the pulses obey unsteady-state, compressible-flow theory and thus provide a measure of both transmissibility (kh/µ) and storage (Fch). In additian, the method can be used qualitatively to describe communication across faults and between zones, and direction and tnagnitude of fracture trends. INTRODUCTION To obtain maximum usefulness of new reservoir analysis methods as well as to aid the field engineer in understanding local reservoir anomalies, improved methods are needed to describe heterogeneities in specific reservoirs. Optimum well spacing, equipment specifications, well completion design and especially the economics of pressure maintenance and secondary recovery programs depend on the extent and location of the heterogeneities that affect flow behavior in the field. One method for obtaining a measure of areal reservoir heterogeneity is an interference test. In the simplest interference test. constant-rate production or injection is initiated at one well and the effect of this flow is measured as pressure vs time at another well. Thus, during interference tests the flow characteristics of the formation are determined in situ. Despite their obvious usefulness in reservoir delineation. interference tests have not enjoyed frequent usage. Reasons for this have been the weeks or months required in many fields to obtain a pressure response measurable with conventional gauges, and the interruption of routine field operation during the field-wide shut-in normally required during these long times. Also, only average properties of the relatively large volume of the reservoir disturbed during these long times can normally be obtained — variations in properties between individual wells cannot be delineated. To eliminate these drawbacks of conventional tests, a special reservoir description technique called pulse testing' has been developed. Pulse-testing has several advantages that make it more convenient and practical for field use than interference tests. Valid tests are more certain because use of a series of flow disturbances gives rise to a diagnostic pressure response that can more readily be distinguished from unknown trends in reservoir pressure and other "noise." The time required is only a fraction of that for an interference test because a special, high-sensitivity differential pressure gauge can detect a much smaller pressure change. Variations in properties between individual wells can be delineated because of the relatively small volume of the reservoir disturbed during these short times. Finally, wells other than the pulsing and responding wells do not have to be shut in or carefully regulated.

Jan 1, 1967

By D. G. Westlake

THE structure observed in thin foils by transmission electron microscopy is not necessarily representative of the initial bulk material. We have shown that hydrogen, originally present in a specimen of vanadium, niobium, or tantalum, can be concentrated by the thinning operation used to prepare foils from the bulk materials.' These foils exhibited domain walls indicative of a tetragonal distortion of the bcc unit cells, probably caused by ordering of the hydrogen in preferred interstitial sites. We believe this ordering does not occur at room temperature in the bulk material which contains less than 1 at. pct H. In a continued effort to prepare metal foils whose hydrogen concentrations remain constant during preparation, we have developed some new chemical and electrothinning techniques for vanadium. Each of the procedures presented in Table I produced foils that were thin enough for transmission electron microscopy. The experiments described below were performed to test the effect of each thinning procedure on hydro-

Jan 1, 1968

By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

By H. M. Morse

There was little change in the oil and gas industry in Mississippi during the year 1938. No new fields were discovered and the production from the Amory field was nil. In the Jackson gas field six wells were drilled and production was obtained in each instance, but none of these wells increased the area from which the gas is produced. Outside the Jackson gas field nine wells were drilled, of which details are given in the accompanying table. The seeming lack of activity in Mississippi belied what was actually happening, for a great many geophysical crews of the major companies were active in all parts of the state. There were approximately 65 structures mapped and for the most part these have been leased. It is believed that 1939 will see an increase in wildcatting over a large part of the state.

Jan 1, 1939

Delay in classifying the war minerals claims geographically and by minerals' has resulted because a part of the claims is in the hands of the commission which is holding hearings at points easy of access from the mining districts. It was necessary for the commission to take many claims for use at these hearings. Twenty days will be allowed claimants to file typewritten or printed briefs based on the record made by the commission's findings. At the end of twenty days, the case will be finally submitted to the Secretary of the Interior. No new facts will be considered, those which have been submitted to the commission only being given consideration. The Attorney General has issued a decision whereby only such claimants as were directly requested by the government to start operations will receive consideration under the War Minerals Act.

Jan 9, 1919

By H. M. Morse

There was little change in the oil and gas industry in Mississippi during the year 1938. No new fields were discovered and the production from the Amory field was nil. In the Jackson gas field six wells were drilled and production was obtained in each instance, but none of these wells increased the area from which the gas is produced. Outside the Jackson gas field nine wells were drilled, of which details are given in the accompanying table. The seeming lack of activity in Mississippi belied what was actually happening, for a great many geophysical crews of the major companies were active in all parts of the state. There were approximately 65 structures mapped and for the most part these have been leased. It is believed that 1939 will see an increase in wildcatting over a large part of the state.

Jan 1, 1939

By Kenneth N. Weaver

Portland cement can be made from relatively abundant industrial minerals and rocks, and this may explain why cement producers placed little emphasis on geology during the early days of the industry. After World War II, however, the industry began to recognize the need for geological exploration, and some of the larger companies began to build a permanent geological staff. This development had its roots in the following factors: Rapid expansion of the industry; closing of many cement plants due to inadequate raw materials; necessity for upgrading the quality of portland cement; and the increasingly large capital investment required to build new cement plants, which in turn, required a higher degree of accuracy in reserve calculations. Whereas the geologist's function during the active expansion of capacity was primarily in exploration, one of his major functions today is the development of existing reserves.

Jan 1, 1965

Elected Died 1895 *ABBOTT, AI ATTHUR 1908 1882 *ABBOTT, ARTHUR V 1906 1905 * ABE, MASAYOSHI 1909 1903 * ADAMS, CHARLES C. 1905 1906 * ADAMS, JOHN C. 1913 1905 * ADAMS, WILLAMS 1909 1903 * ADAMS, W. EDWARDS 1910 1884 *ADDY, MATTHEW 1896 1906 * AFFLECK, WILLIAM A. 1911 1889 * AKERS, WILLIAMS A. 1906 1905 * ALABASTER, RUPPERT C. 1911 1899 * ALBERGER, LOUIS R. 1911 1894 *ALLEN R B 1896 1905 * ALLEN, R. SCOTT 1906 1874 * AMIOT, H. 1892 1886 *AMSLER, CARL 1894 1898 ** ANDRSON, JOHN W 1905 1895 *ÅNGSTROM, CARL 1901 1887 * ARCHBALD, JAMES 1910 1900 * ARLETT, GEORGE H 1906 1895 *ARMSTRONG, JOHN F 1898 1882 *ARNOLDS, HUGO 1886 1875 *ASHBURNER, CHARLES A 1889 1872 *ASIIBURNER, WILLIAM 1887 1883 *ATKINS, C M , JR 1885

Jan 1, 1917

By Edward A. Loria

A SERIES of papers on the study of austenite grain A size in cast steels has been published recently.'" These studies show that in the as-cast state, the austenite grains are quite large, for they form as the steel freezes at a very high temperature, but a simple reheating above the critical range produces a new set of austenite grains which, in many instances, is finer than ASTM grain sire No. 8. Furthermore, there is no apparent relationship between as-cast austenite grain size and subsequent grain size produced by heat treatment. The as-cast austenite grain size can be determined easily in plain carbon and low alloy steels which produce a continuous grain boundary f errite envelope in the as-cast structure. In the case of cast steels whose alloy content produces greater hardenability and suppresses the proeutectoid ferrite transforma-

Jan 1, 1952

By C. C. Harris

The 3-parameter equation* was introduced1 as having the necessary form and flexibility for describing the major features of size distribution curves. Also, Eq. 1 was shown to contain most of the widely used 2-parameter equations as special cases. Special methods are necessary in order to determine the parameters of 3-parameter equations by graphical means. The procedure given previously required double graphical interpolation followed by regraphing the interpolated data. The theoretical basis of the method was a difference equation eliminating y. Several other methods for obtaining the parameters have been under development and one method appears to overcome the disadvantages of the earlier method and satisfies several procedural requirements. The points in favor of the new method as compared to the earlier method are as follows: 1. Estimation of the quality of fit is direct, and is in fact an essential part of the procedure. 2. The data is plotted directly without the necessity of interpolation from a graph. 3. The method makes use of Rosin-Rammler2 paper which because of expanded scaling in the coarse sizes leads to improved accuracy1 as compared with the log-log plot for the Gates3-Gaudin4-Schubann5 representation. 4. There is a gain over the earlier method in overall accuracy and in simplicity.

Jan 1, 1970

Ellsworth Daggett, who joined the Institute in 1873, and had beeu a prominent figure in the mining profession of Utah and other Western states for many years, died in San Francisco, Jan. 5, 1923. Mr. Daggett was a contemporary and intimate friend of Clarence King, James D. Hague, R. W. Raymond, and other Nestors of the mining engineering profession prominent in the last quarter of the nineteenth century. He was born at Canandaigua, N. Y., May 24, 1845; graduated from Sheffield Scientific School in 1864; pursued post-graduate courses there for two years, and for one year at the Bergakademie, in Berlin. He was in active practice as mining engineer from 1866 to 1914, but devoted most of his time during the World War to the perfecting of a submarine torpedo. He was connected with the United States Geological Exploration of the Fortieth Parallel in 1870. The plates illustrating mining industry, Volume III of the reports of that survey, were engraved from drawings obtained in the field during progress of the survey and prepared for the engraver by Mr. Daggett. He operated the Winnamuck mine and smelter at Bingham Cation, Utah, in the early seventies; the mines and mill at Cusihuiriachic, Chihuahua, 18867; and the Berlin mine near Austin, Nevada, 1904-6. On June 24, 1874, Mr. Daggett married Miss June Spencer, of Salt Lake City, who survives him, residing in New Haven, Corn. Appointed United States Surveyor General for Utah by President Harrison, in 1888, he was the first engineer to hold that office in Utah. He reorganized the mineral division of the office, required the courses of mineral surveys to be referred to the true meridian determined by solar or stellar observations, and did much to improve the accuracy and reliability of such surveys. Mr. Daggett was a member of the Alta and University Clubs of Salt Lake City, and president of the latter from 1890 to 1892; he was also a member of the Century Club, New York. Through his instrumentality, irrigation was brought to considerable tracts of land in northeastern Utah, and Daggett County of that state is named for him. Re wrote numerous technical papers, and an economic review entitled "A Quarter of a Century of Prices," in which was shown the close relation

Jan 1, 1923

Ellsworth Daggett, who joined the Institute in 1873, and had beeu a prominent figure in the mining profession of Utah and other Western states for many years, died in San Francisco, Jan. 5, 1923. Mr. Daggett was a contemporary and intimate friend of Clarence King, James D. Hague, R. W. Raymond, and other Nestors of the mining engineering profession prominent in the last quarter of the nineteenth century. He was born at Canandaigua, N. Y., May 24, 1845; graduated from Sheffield Scientific School in 1864; pursued post-graduate courses there for two years, and for one year at the Bergakademie, in Berlin. He was in active practice as mining engineer from 1866 to 1914, but devoted most of his time during the World War to the perfecting of a submarine torpedo. He was connected with the United States Geological Exploration of the Fortieth Parallel in 1870. The plates illustrating mining industry, Volume III of the reports of that survey, were engraved from drawings obtained in the field during progress of the survey and prepared for the engraver by Mr. Daggett. He operated the Winnamuck mine and smelter at Bingham Cation, Utah, in the early seventies; the mines and mill at Cusihuiriachic, Chihuahua, 18867; and the Berlin mine near Austin, Nevada, 1904-6. On June 24, 1874, Mr. Daggett married Miss June Spencer, of Salt Lake City, who survives him, residing in New Haven, Corn. Appointed United States Surveyor General for Utah by President Harrison, in 1888, he was the first engineer to hold that office in Utah. He reorganized the mineral division of the office, required the courses of mineral surveys to be referred to the true meridian determined by solar or stellar observations, and did much to improve the accuracy and reliability of such surveys. Mr. Daggett was a member of the Alta and University Clubs of Salt Lake City, and president of the latter from 1890 to 1892; he was also a member of the Century Club, New York. Through his instrumentality, irrigation was brought to considerable tracts of land in northeastern Utah, and Daggett County of that state is named for him. Re wrote numerous technical papers, and an economic review entitled "A Quarter of a Century of Prices," in which was shown the close relation

Jan 1, 1923

By James Kemp

IN THE Alumni catalogue of Amherst College and with the Class of 1848 is recorded the name of Louis Palemon Ledoux, who on graduating studied for the ministry at the Union Theological Seminary in New York and was ordained by the Presbyterian church. Louis Palemon Ledoux entered college from Louisiana and, as his name implies, was of French ancestry. His departure from the traditions of his forebears in register-ing in a Protestant college and later becoming a Presby-terian minister brought about some alienation from his family which, however, softened with the passage of years and disappeared between later generations. In time the Rev. Louis P. Ledoux was married to Kate C. Reid of New York City and was stationed for a year at Newport, Ky., where on Nov. 2, 1852, his oldest son Albert Reid Ledoux was born. The next year, the family moved to Monroe, Mich., where for two years the young clergyman was pastor of the Presbyterian church. A call to Richmond, Va., then led them to live from 1855-1858 in the, Virginia capital, but the father became afflicted with what was then regarded as a mysterious ailment, malaria, and to escape it migrated in 1858, when the young boy Albert was a little over five years old, to Cornwall-on-Hudson, and became pastor of the Presbyterian church in the lower village near the river. In 1861 he was honored with the degree of D.D. from the State Uni-versity of Indiana. Some years later throat trouble compelled the Rev. Dr. Ledoux to give up preaching and led him to establish a school for boys, known as the Storm King School, above Cornwall, on the slopes of Storm King Mountain. As a boy Albert Ledoux roamed the woods of Storm King and became deeply attached to this .wonderful hillside, commanding as it does an extended view of Newburgh Bay to the north and the remoter reaches of the Hudson. In his later years he built his home on its slopes and continued to roam its woods for his recreation. In later years, also, the writer used to look each October for the fringed gentian which Dr. Ledoux gathered in some secret nook to wear in his lapel. In the Storm King school, Albert Ledoux and his brother Augustus Damon, seven years younger, were educated and entered the School of Mines of Columbia College.

Jan 12, 1923

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wilbarger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature arc in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1939 With the later stages of development being reached in the K.M.A. field during the first half of the year, some 400 fewer producing wells were drilled in North Texas in 1939 than in 1938, when some 1750 wells were drilled. Despite this decrease in activity, production in 1939 increased about 3½ million barrels over 1938 figures, and at the end of the year the oil reserves were somewhat larger than on the first of the year. As is usually characteristic of the district, this resulted from the discovery of a large number of relatively unimportant fields. Owing principally to no appreciable abatement in wildcat drilling, more new fields and extensions to old fields were discovered this year. Although none of these discoveries was of such magnitude as to be important to the oil industry, the new developments in Montague and Cooke Counties portend greater and probably more important operations in these areas.

Jan 1, 1940

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wilbarger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature arc in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1939 With the later stages of development being reached in the K.M.A. field during the first half of the year, some 400 fewer producing wells were drilled in North Texas in 1939 than in 1938, when some 1750 wells were drilled. Despite this decrease in activity, production in 1939 increased about 3½ million barrels over 1938 figures, and at the end of the year the oil reserves were somewhat larger than on the first of the year. As is usually characteristic of the district, this resulted from the discovery of a large number of relatively unimportant fields. Owing principally to no appreciable abatement in wildcat drilling, more new fields and extensions to old fields were discovered this year. Although none of these discoveries was of such magnitude as to be important to the oil industry, the new developments in Montague and Cooke Counties portend greater and probably more important operations in these areas.

Jan 1, 1940

Today, the employment of the modern hammer drill, using hollow steel, with air or water to expel the cuttings from the drill hole, is the rule rather than the exception in practically all rock-drilling operations. There is considerable carelessness in the matter of keeping the hole in the drill steel properly opened. Plugged steels wholly or partially, prevent proper operation of the drill, whereby drilling speed is retarded, water tubes are bent or broken, and time is lost in tink-ering, or, as often happens, the drilling gang is idle while someone makes a trip to the shop after another drill steel or water tube. To relieve this condition, the Ingersoll-Rand Company has developed, as an auxiliary to the Leyner sharpener, a new device-the Leyner shank and bit punch.

Jan 4, 1918

By H. D. Kessler, Joseph B. McAndrew

WHEN there is occasion to make structural use of metals at temperatures above 900°C (1652°F), the choice of alloys is severely limited, and those materials which meet special requirements as to density, strength, toughness, and resistance to creep, oxidation, or fatigue at such temperatures are at a premium. Any new type of high temperature alloy which is found to be outstanding with respect to several of these properties is therefore likely to find special applications for which it is uniquely advantageous as compared to other alloys. Such is the case with the 7 titanium-aluminum alloys. This y phase is an intermediate phase based on the composition TiAl, and extends from about 35.5 to 44.5 wt pct Al at temperatures up to 1000°C, above which the field broadens to include 60 pct A1 at 1340°C.' The alloys of principal interest have a narrow melting range, with 7 forming by the peri-tectic reaction, melt + ß=y at about 1460°C. Unlike most intermediate phases, the binary alloys containing titanium and aluminum in approximately equiatomic proportion possess low room temperature hardness,' in addition to which they have low density, good resistance to oxidation, and relatively high modulus of elasticity.' Unpublished work done at Armour Research Foundation showed

Jan 1, 1957

[University or College Alabama, University of, University, Ala. California University of Berkeley Cal Carnegie inst. of Technology Pittsburgh Pa. Case School of Applied science, Cleveland, Ohio Colorado School of Mines Columbia University New York City Harvard University, Cambridge. Mass.]

Jan 1, 1928

By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967