Search Documents

By Hans Lundberg, Theodor Zuschlag

Based upon an instrumental improvement, a new development has taken place in the art of electrical prospecting, and some remarkable results have already been obtained with regard to potential exploration. In order to visualize the importance of this development, it is deemed advisable to review briefly the fundamental facts about potential surveys. Potential exploration may be carried out qualitatively or quantitatively. Qualitative investigations are made by determining and plotting on a map points of equal potential, whereby any anomalies are revealed, without, however, much clue to their magnitude. Quantitative investigations determine the variations of potential or potential drop, and thus show not only the location of the anomalies, but also their magnitude. Figs. 1 to 6 illustrate the influence of simple types of ground inhomo-geneities, assuming one effective exciter potential only. Such a condition can be closely realized by connecting an electric current source to two electrodes, one of which is located at a great distance. Assuming uniform ground resistivity, the resultant potential distribution mar be represented by concentric spheres. Any change from the normal condition causes a characteristic distortion of the spheres, which becomes different for different types of resistivity variation. The series of Figs. la to 6a illustrates schematically results of qualitative investigations and series lb to 6b results of quantitative investigations. Figs. 1 and 2 picture the well-known case of local resistivity variations normally encountered in ore prospecting. Figs. 3 and 4 show the reactions caused by more or less vertical resistivity contacts and Figs. 5 and 6 refer to the problem of ground-water and bedrock investigations where the resistivity contact is horizontal or nearly SO. It is evident from Figs. 5a and 6a that qualitative measurements do not permit an identification of such general geological features as widespread horizontal strata, because the resultant contraction or expansion of the equipotential circles at the surface cannot be recognized without quantitative determinations. On the other hand, qualitative measurements are well suited for the exploration of local or lateral resistivity

Jan 1, 1932

By Herman Dykstra, R. L. Parsons

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

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

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

Jan 1, 1951

By J. E. Pavlick, A. G. Guy

The total creep of tin alloys containing antimony in solid solution was observed to decrease with increase in antimony content. However, near the solubility limit an anomalous maximum in deformation was. found, in agreement with similiar observations by Bochvar. IT has long been recognized that alloys may deform more rapidly under stress if there is a tendency for a phase change or other structural change to occur simultaneously. However, the phenomena involved are complex and in some instances the opposite effect, strengthening, may result.' This area of research has not attracted much interest in the western world, and although Russian investigators have studied it for the past 15 years their work has not received due attention here. Recently diametrically opposing views on one aspect of this problem have been espoused by two Russian investigators, Kornilov and Bochvar. The question is this: in certain binary alloys tested in creep at the temperature where the solute is at the limit of solid solubility, does the incipient formation of the second phase strengthen or weaken the alloy? Korni-lov's arguments in favor of strengthening were presented at the 1954 Symposium at the National Physical Laboratory, =Creep and Fracture of Metals at High Temperatures.The most recent statement of Boch-var's theory of weakening is in Oding's new book on creep and rupture.3 Although Bochvar agrees that strengthening occurs in some alloy systems, he argues that in certain alloys an anomalous weakening is observed. However, the extensive work of Korni-lov's group on creep properties of alloy systems has not revealed any anomaly of this type, but instead has tended to refute Bochvar's theory. This clear-cut controversy offered a good opportunity for a simple experiment to resolve the problem. The experiment and its results supporting Bochvar are the subject of this paper. However, it will be helpful first to sketch the present status of the larger question of the effect of a phase change or other structural change on plastic deformation. PREVIOUS WORK One of the first researches in this area was by Pfei1,37 who investigated the creep resistance of an 80 Ni-20 Cr alloy containing varying amounts of titanium. He found that the resistance to creep increased rapidly as the solid solubility limit in the alloy at 775'c was approached and slightly exceeded. With further addition of titanium the creep resistance decreased, presumably because of precipitation effects. Bochvar's first work in this field was a study in 1945 of "superplasticity" in zinc alloys containing 15 to 25 pct Al.4 He found that alloys quenched from about 400 had anomalously low hardness when tested below this temperature. The following year, in a paper on the dependence of mechanical properties on the composition and structure of alloys,5 he extended some observations of Kurnakov to predict that at high temperatures of testing the hardness values for solid-solution alloys might be lower than those for the component metals. He also pointed out the influence of changes in solidus temperature in affecting curves of hardness vs composition, and he

Jan 1, 1962

By AIME AIME

BEFORE proceeding with the papers scheduled for the ore and foundry session*, the teller's report on the election of officers for the ensuing year was presented, a; follows: Chairman. G.C. F. MacKenzie; vice-chairmen, C.S. Robinson, J. T. MacKenzzie, C. E. Meissner; executive committee, A. L. Field, R. F. Harrington, E. F. Kenney lit. Waterhouse announced that the fall meeting will be devoted to alloy steel. This meeting will be held in Chicago the week of Sept. 22 in connection with the National Metal Congress. He also announced that oxygen in steel will be the central idea of the meeting which will be held in New York next February. The first paper, entitled "Sintering Limonitic Iron Ore at Ironton, Minn.," was presented by Perry G. Harrison (T. P. 284), the author. Sintering was first un¬dertaken in 1024 to treat Cuyuna range iron and manganiferous ores low in silica and high in moisture and containing objectionable qualities of fine... A Dwight-Lloyd machine was first installed. This machine was replaced by a larger one having a width of 72 in. The power cost was decreased from about $11.22 per ton of sinter on a 42-in. machine to about X0.14 for the 72-in. machine. The tons of sinter per man-shift was increased from 11.86 to 16.77. Improvements embodied in the larger plant reduced the cost of sintering to $0.41. The analyses of iron ore and manganiferous ore and the sinter produced from these materials was used to show the increase in value at the mine resulting from sintering. Crude iron ore actually unsalable was increased in value f.o.b. mine from a theoretical figure

Jan 1, 1930

By Morris Muskat

TEe method of R. W. Moore' for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

By Morris Muskat

TEe method of R. W. Moore' for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

By H. R. Thresh

An oscillational vis cometer has been constructed to measure the viscosity of liquid metals and alloys to 800°C. An enclosed cylindrical interface surrounds the molten sample avoiding the free surface condition found in many previous measurements. Standardization of the apparatus with mercury has verified the use of Roscoe's formula in the calculation of the viscosity. Operation of the apparatus at higher temperatures was also checked using molten lead. Extensive measurements on five different samples of zinc, of not less than 99.99 pct purity, indicate i) impurities at this level do not influence the viscosity and ii) the apparatus is capable of giving reproducible data. The variation of the viscosity ? with absolute temperature T is adequately expressed by Andrade's exponential relationship ?V1/3 = AeC/VT , where A and C are constants and V is the specific volume of the liquid. The values of A and C are given as 2.485 x 10-3 and 20.78, 2.444 x 10-3 and 88.79, and 2.169 x 10-3 and 239.8, respectively, for mercury, lead, and zinc. The error of measurement is assessed to be about 1 pct. Prefreezing phenomena in the vicinity of the freezing point of the zinc samples were found to be absent. AS part of an over-all program of research on various phases of melting and casting nonferrous alloys, a systematic study of some physical properties of liquid metals and their alloys was undertaken in the laboratories of the Physical Metallurgy Division.1,2,3 The most recent phase of this work, on zinc and some zinc-base alloys, was carried out in cooperation with the Canadian Zinc and Lead Research Committee and the International Lead-Zinc Research Organization. One of the properties investigated was viscosity and the present paper gives results on pure zinc; the second part, on the viscosity of some zinc alloys, will be reported separately. Experimental interest in the viscosity of liquid metals has virtually been confined to the past 40 years. The capillary technique was already established as the primary method for the viscosity of fluids in the vicinity of room temperature; all relevant experimental corrections were known and an absolute accuracy of 1 to 2 pct was possible. Ap- plication of the capillary method to liquid metals creates a number of exacting requirements to manipulate a smooth flow of highly reactive liquid through a fine-bore tube. Consequently, the degree of precision usually achieved in the high-temperature field rarely compares with measurements on aqueous fluids near room temperature. However, the full potential of the capillary method has yet to be explored using modern experimental techniques. As an alternative, many investigators in this field have preferred to select the oscillational method. Unfortunately, the practical advantages are somewhat offset by the inability of the hydrodynamic theory to realize a rational working formula for the calculation of the viscosity. In attempting to overcome this restriction many investigators have employed calibrational procedures, even to the extent of selecting an arbitrary formula for use with a given shaped interface. However, where calibration cannot be founded on well-established techniques, the contribution of such experiments to the general field of viscometry is questionable. A critical appraisal of the viscosity data existing for pure liquid metals reveals a somewhat discordant situation where considerable effort is still required to establish reproducible and reliable values for the low-melting point metals. The means of rectifying this situation have gradually evolved in recent years. Here, the theory of the oscillational method has undergone major advances for both the spherical and cylindrical interfaces. The basic concepts of verschaffelt4 governing the oscillation of a solid sphere in an infinite liquid have been adequately expressed by Andrade and his coworkers.5,6 Employing a hollow spherical container and a formula, which had been extensively verified by experiments on water, absolute measurements on the liquid alkali metals were obtained. The extension of this approach to the more common liquid metals has been demonstrated by culpin7 and Rothwel18 where much ingenuity was used to surmount the problem of loading the sample into the delicate sphere. Because of the elegant technique required to construct a hollow sphere, the cylindrical interface holds recognition as virtually the ideal shape. On the other hand, loss of symmetry in one plane increases the complexity of deriving a calculation of the viscosity. The contributions of Hopkins and Toye9 and Roscoe10 have markedly improved the potential use of the cylindrical interface in liquid-metal viscometry. The relatively simple experi-

Jan 1, 1965

By Newell Alford

AT its meeting in the fall of 1937, the Executive Committee of the Coal Division considered the growing scarcity of young engineers entering coal mining with serious intentions. This scarcity was the cause of con-siderable alarm and a committee consisting of C. T. Hayden, E. A. Holbrook, C. E. Lawall and L. E. Young, with the writer as chairman, was appointed to gather factual data on the current trend. A questionnaire1 was designed and mailed to the heads of the 60 mineral technology schools listed by Prof. W. B. Plank in his article in September 1937.2 Replies were received from 46 institutions, not all from heads of coal-mining courses but all from men that at one time or another have had experience with some kind of coal-mining curricula and know current student impressions. Our committee is indebted to all of these gentlemen for their cooperation. Our committee hoped by this means to quickly reach the root of the trouble and make a set of comprehensive recommendations to the Coal Division for relieving the industry immediately from the growing dearth of youth who yearn for coal-mining careers, but the condition is more serious than at first diagnosed. We must now refer the question back to the Coal Division, with the recommendation that the Division get the industry's permission for still another major operation on its frame of mind. In addition to 10-year statistics on the first pay received by graduates in coal mining and other technical work, we requested enrollment data for 20 years from all schools with either mining engineering or mineral technology curricula. Nine leading questions were also plied, as shown in the Appendix. Every one of the answers was significant and inter-esting. Fortunately, we encountered positive frankness that was extremely helpful.

Jan 1, 1938

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. J. Charles

PREVIOUS study' of simple impact systems indicated that energy required for fracture and size reduction of brittle materials is greatly dependent on the type of loading that is employed. In this regard it was postulated that fracture and size reduction of a brittle specimen might be accomplished by a high velocity impact at an energy level at which a low velocity impact would leave the specimen relatively undamaged. The finite time required to propagate energy away from the point of loading of an impacted object to other parts of the object and to its supports may permit a concentration of energy at the point of impact if the rate of loading is high. Localizing of energy at the point of impact could quickly initiate fractures that would propagate through the impacted material along with the traveling stress waves. As the cracks form, the initially absorbed strain energy would be released and portions of it travel ahead of the wack tips as stress waves. These secondary stress waves, combined with the initial stress waves derived from the impact, would produce high localized strain conditions in front of the fracture zone. The fracture zone would propagate and the specimen shatter. High rates of loading are brought about by short impact times, in turn obtained by employing high velocity projectiles that are of small mass compared to the impacted object. In the case of a low velocity impact, at an energy level equal to that of a high velocity impact that causes fracture, loading rate would be relatively

Jan 1, 1957

By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The microhardness of single crystals of tungsten disilicide has been investigated by the Knoop method. The average random room-temperature hardness of the WSi, matrix was 1350 kg per sq mm. Hardness crnisotropy was noted with respect to plane and indenter orientation as determined by single-crq.stal X-rny studies. Annealing at 1600" and 1800°C decreased the average hardness to 1310 and 1230 kg per sq tnm, respectively, and produced a second phase identified by X-ray diffraction and electron-microprobe analysis to be wSio.7. Ball-impact experiwzents produced rosettes at 850°C. Optical and electron microscopy showed evidence of slip and cross slip and twinning produced by microhardness indentations. Prismatic (100), [001] slip was found and cor~elated with hardness data. THE present study was undertaken to investigate the hardness anisotropy of as-grown and annealed single crystals of tungsten disilicide. The existence of the silicide WSiz in the W-Si system has been well-established and its structure thoroughly investigated zachariasen2 found WSi, to have a tetragonal C type of structure, similar to that of MoSi, with lattice parameters a = 3.212A, Kieffer et al. studied the W-Si system and measured the density and microhardness (at a 100-g load) of both polycrystalline WSi, and WSi,.,. The values found were 9.25 g per cu cm and 1090 kg per sq mm for WSi,, and 12.21 per cu cm and 770 kg per sq mm for WSi0.7, respectively. According to Samsonov et a1.5 the microhardness of polycrystalline WSi2 is 1430 kg per sq mm (at a 120-g load). EXPERIMENTAL The WSi, single-crystal boules investigated in this paper were grown by a Verneuil-type process using an electric arc by the Linde Division of the Union Carbide Corp.6 The largest specimens were 8 mm in diameter by 16 mm long. The crystals had an average density of 9.01 g per cu cm with a tungsten • silicon content of 99.9 wt pct. The major impurities were: 87 ppm O, 41 ppm N. 54 pprn C, 500 ppm Zr, 50 ppm Na, and 50 ppm Mn. The crystals were silicon-poor, the average silicon content being 22.20 pct (stoichiometric value is 23.40 pct), and tungsten-rich, the average tungsten content being 77.70 pct (stoichiometric value is 76.60 pct). As-received single crystals were ground and analyzed by powder X-ray diffraction technique using Cu Ka radiation. Laue and layer line rotation patterns were obtained on cleaved sections of WSi, single crystals. Electron-microprobe traverses of representative crystals were done using a Phillips-AMR electron microanalyzer. Carbon replicas were used to prepare electron micrographs. This work was done with a JEM-6A electron microscope. Prior to the metallographic examination, the specimens were mounted in Lucite and then polished for short times on polishing wheels using 9-, 3-, and 1-p diamond-grade pastes. Finally they were fine-polished with Linde A powder for 24 hr on a Syntron vibratory polisher. The samples were etched with 4H 2 O:1HF:2HNO3, which is a medium fast-acting etchant. The combination 1HF:2HNO3:5 lactic acid is also a satisfactory etchant. Annealing runs for selected specimens were made at 1600" and 1800°C for 3 hr at 1.0 to 3.0 x 10-5 mm Hg. A Brew tantalum resistance furnace with WSi2 powder for setters was used. The WSi2 powder was the same as that used for the crystal growth. Temperatures were measured with a calibrated W, W-26 pct Re thermocouple and a microoptical pyrometer. Powder X-ray diffraction, emission spectrographic, and electron-microprobe analyses were done after the annealing runs. For microhardness measurements a Tukon Microhardness Tester Type FB with a Knoop indenter was used. Although measurements were taken at loads ranging from 25 to 1000 g, the 100-g load was chosen as the standard load. All measurements were taken at room temperature. Only indentations of cracking classes 1 and 2 were considered.' DISCUSSION OF RESULTS Powder X-ray diffraction analysis showed the as-received crystals to be single-phase WSi2. Laue and layer line rotation patterns obtained on cleaved sections of WSi2 single crystals proved them to be tetragonal WS 2 2 The results also indicated that the c axis of the crystal was oriented parallel to the boule or growth axis. Electron-microprobe traverses across the matrix of the as-grown crystals showed them to be homogeneous WSi,. Optical and electron microscopy of etched crystals, however, revealed that they contained minute amounts of the "golden" and the "blue" second phases as opposed to the "white" or WSi2 phase. These two second phases were concentrated in inclusion and etch-pit

Jan 1, 1965

By Alexander L. Field

IN a previous paper,' the experimental methods used and some of the results obtained in an extensive investigation of steels containing zirconium were described. The present paper considers in greater detail one of the most interesting of these effects, namely, the elimination of " red shortness" and the occurrence in steel of a compound of zirconium and sulfur. A consideration of the actual percentages of zirconium, manganese, and sulfur in numerous steels in the light of behavior during rolling has led to new conclusions of the most practical import regarding the reciprocal relationships of these elements. The microscopic examination of high-sulfur steels containing zirconium has also been productive of interesting results. Before discussing the experimental data in question, it may be stated, briefly, that the rettetion between zirconium and sulfur in molten steel may be represented by the simple equation, Zr + 25 = ZrS², and that the zirconium sulfide thus formed occurs in the finished steel in the form of gray-colored inclusions, closely resembling manganese sulfide and, like the latter, exhibiting plasticity at rolling temperatures. Molten steel containing zirconium retains such a negligibly small amount of oxygen in solution that the foregoing reaction goes to completion. Hot-rolling Properties of High-sulfur Steels with and without Zirconium The chemical composition of twenty-eight steel ingots embracing eleven heats made in a basic-lined electric furnace is shown in Table 1. The practice followed in the manufacture of these high-sulfur steels was described in the previous paper. Table 1 also gives the behavior of the

Jan 1, 1924

By Emile Gyss

THE speed of drilling rock has become an impor-tant factor in mining operations, while the place-ment of holes, kind, and quantity of explosive used. are equally important. These are a function of the rock hardness and toughness. Both of these fac-tors must be considered in compiling a table that will enable a mine operator or engineer to estimate drilling speeds in a given rock, knowing its hardness, and from its toughness, the dynamite required. The hardness of a homogeneous rock may be defined as its resistance to a penetrating medium, such as a drill-steel bit, and toughness, its resistance to with-stand rupture by the tearing apart of its minerals or parts of the same mineral. Rock hardness, as it has here been defined, is a function of the hardness of the component grains composing it, as well as grain size, shape, arrangement, and binding minerals. Rock tough-ness depends on substantially the same factors, but is measured by a totally different method. The units in which rock hardness is usually ex-pressed are either relative values or alphabetical desig-nations which carry no definite quantitative meaning. R. M. Raymond has suggested the measurement of com-posite rock hardness, based on mineral hardness as ob-tained by the Moh scale. This is done by multiplying the percentage of each mineral in a rock by the Moh mineral hardness and dividing by 100. These values convey a clearer conception in the minds of men in-terested in rock work -and are the basis of the units used in Tables 1 and 2. The hardness of rocks as it has been variously de-fined may be determined by different methods. The first method is one in which the proportionate average of the hardness of minerals making up a rock is the basis for classification. The other factors of grain size, shape, arrangement, and binding power are not considered.

Jan 6, 1927

By C. J. Huffman

MAGNESIUM alloy tubing and hollow shapes are finding increasingly wider usage in practical applications today. Square and rectangular tubing and hollow shapes find [ ] greater diversification in use than standard round tubing. Typical applications are roller conveyors, ladder rungs, spools, furniture, tank car loading tubes, athletic equipment, and business machine parts. In general, the amount of tubing and hollow shapes produced represent a minor portion of the magnesium extrusion business. The magnesium alloys in which tubing and hollow shapes are being produced together with typical properties are presented in Table I. MI A alloy is a low cost alloy possessing good welding and stress corrosion characteristics together with moderate formability and corrosion resistance. It is widely used for low strength applications. AZ31 B, alloy is used for moderately stressed applications and possesses good corrosion resistance and formability with fair welding characteristics. AZ61 A alloy has slightly higher physical properties than AZ31 B alloy together with good formabil- [ ] ity and corrosion resistance but slightly poorer welding characteristics. AZ80 A, ZK60 A-F, and ZK60 A-T5 alloys are used where the maximum in physical properties is required. AZ80 A alloy possesses fair corrosion resistance but with formability and welding characteristics inferior to' the other alloys. ZK60 A-F and ZK60 A-T5 alloys, while only recently offered for com¬mercial use, are finding favor due, to the higher permissible extrusion rates. These alloys possess greater toughness than AZ80 A alloy and, while of moderate formability at room temperature, are very formable at 300° to 500°F. The major portion of tubing and hollow shape production at the present time is in AZ3I B alloy. Magnesium alloy tubing is commercially available in the as-extruded condition or, in the case of ZK60 A-T5, in the as-extruded and aged

Jan 1, 1951

By R. C. Buehl, J. P. Morris

F. D. Richardson—The authors are to be congratulated on this further contribution to our knowledge of the thermodynamics of the interaction between sulphur and carbon and silicon in liquid iron. As the authors state, the influence of carbon and silicon on the activity coefficient of sulphur in liquid iron is clearly of great importance in the blast furnace, since it must cause a three to fourfold improvement in the partition of sulphur between slag and metal. The influence of increasing temperature in further increasing the activity coefficient of the sulphur in the metal in the blast furnace by increasing the carbon content is also of interest. This effect, however, is probably only part of the reason for the general observation in blast furnace practice, that the sulphur content of the metal is lowered by increasing temperature. Other contributing factors are the lowering of the oxygen potential in the presence of carbon by increasing temperature and the probable increase in the activity coefficient of the lime in the slag for the same reason. The former of these effects, which works via the (CaO) + [S] = (CaS) + [O] equilibrium, might possibly account for a 70 pct improvement in the sulphur partition and the latter might give a further 50 pct improvement. C. Sherman—I would like to compliment the authors on their very careful research. If I may, I would like to show results of calculations on the carbon-sulphur-iron system similar to the ones that were shown in our paper for the silicon-sulphur-iron system. For Fe-S-C ternary system k=PHgs/PH2 x 1/(f1°) (f2°) (%S) where fs = sulphur activity coefficient fs' = fs for Fe-S system of equal pct S f3° = f2/f2 for Fe-S-C ternary system This same analysis has been used on other systems, but the results shown in fie.- 7 are for carbon and silicon. L. S. Darken—I would like to make two brief comments in addition to complimenting the authors on an apparently very precise and accurate investigation. The first is that the present work is in agreement with a calculation by Larsen and myself." Our calculation (much less precise than the present work) was based on: (1) Unpublished work on the sulphur content of molten iron (1.5 pct at 1500°C) in equilibrium with graphite and an iron sulphide slag; (2) the distribution coefficient of sulphur between slag and carbon-free liquid iron. We expressed the result in a form equivalent to log 7. = 0.18 [%C] which gives an activity coefficient (?s.) of sulphur only slightly higher than the authors find and certainly within the precision of the earlier work. My second comment concerns the correlation of the thermodynamic findings with atomistics. A rough pic- ture of the atomic arrangement in the liquid solution is rather easily conceived for this particular liquid solution containing iron, carbon, and sulphur. Carbon has a very much stronger affinity for iron than for sulphur. Hence we may conclude that a sulphur atom will but seldom be adjacent to a carbon atom—since this would be a position of high energy. From the metallic radii of iron and carbon we know that six iron atoms pack neatly around one carbon atom. Thus each carbon atom in retaining this shell of iron atoms (which latter may not be replaced by sulphur on account of the high energy requirement) decreases the available positions for each sulphur atom by six. Hence each atomic percent of carbon decreases the equilibrium sulphur content by 6 pct (of itself). Or, at low concentration each atomic percent of carbon increases the activity coefficient of sulphur by 6 pct. This is in good agreement with the observed increase (6 or 7 pct at low carbon content). It is indeed gratifying to find a case where, by such simple reasoning, quantitative agreement is found between precise data and the modern picture of the atomistics of the metallic state. J. P. Morris (authors' reply)—We would like to point out that there is an error in the equation on p. 322 of the paper. The third equation should read: ½S2 (gas) + H2 (gas) = H2S (gas) The authors wish to thank everyone for the interest they have shown in the paper. In regard to the general observation in blast furnace practice, that the sulphur content of the metal is lowered by increasing the temperature, Dr. Richardson is correct in stating that the cause can be attributed only in part to the increase in activity coefficient of sulphur resulting from the rise in carbon plus silicon content of the metal with rise in temperature. However, this factor is probably an important one. The results of one experiment, performed since this report was written, indicate that at a constant temperature the addition of silicon to a melt saturated with carbon causes an increase in the activity coefficient of sulphur even though the carbon solubility is lowered. In this test, 2.5 pct silicon was added to a melt saturated with carbon and maintained at 1400°C. Although the carbon content dropped from 4.85 to 4.1 pct, the activity coefficient of sulphur was increased by about 20 pct.

Jan 1, 1951

By D. C. Buffum, L. D. Jaffee

THAT the path of brittle fracture in temper brit-tle steel differs from the path in unembrittled steel has been known for some years1 More recently it has been recognized that alloy steels, at least, display two forms of temper brittleness1 which may be called upper-nose and lower-nose. No experimental evidence has been published, however, to show that the two forms can be distinguished by simple inspection of brittle fractures. Fig. 1 is a photograph of the fractured surface of a V-notch Charpy specimen of SAE 3140 steel in which temper brittleness developed during heat treatment in the lower-nose temperature range.' The steel was austenitized 1 hr at 900°, tempered 1 hr at 675", and embrittled 48 hr at 500°C, with water-quenching after each treatment. The temperature of transition from ductile to brittle fracture in the Charpy test was + 2°C (criterion of transition: 100 pet fibrous). The hardness was Re 25; the austenite grain size ASTM 8. This specimen was broken at 150°C in the standard Charpy test and absorbed 6.6 ft-lb; its fracture was rated 0 pet fibrous. Fig. 1 shows that the fracture appeared rough to the naked eye. At the side of the specimen away from the notch (the side which was in compression during the test), the surface as a whole deviated sharply from a plane. At higher magnification, X60, the surface gave

Jan 1, 1959

By Messrs. von Jonstorff

Continued Discussion of the Paper of Messrs. von Jonstorff, Blair, Dillner and Stead, presented at the New York Meeting of the Iron and Steel Institute, October, 1904.* (Bethlehem Meeting, February, 1906.) CLEMENS C. JONES, Richmond, Va. (communication to the Secretary+) :-In the chapter of this paper entitled "Method for the Determination of Phosphorus," by Andrew A. Blair, a form of the reductor used by Mr. Blair is illustrated. This form was employed by me in my earliest experiments, and abandoned after my adoption of the final apparatus described in my paper on the subject in 1889. The results reported by Mr. Blair are very closely accordant; but my experience was that, in the use of this form, a loss of the solution, amounting to almost a cubic centimeter, was occasioned by minute bubbles of hydrogen rising to the surface, and there exploding. My final reductor was designed to prevent this loss; and the most satisfactory results were obtained with a reductor having the open cup replaced by a bulb-shaped receptacle, provided with a glass stopper, similar to that of a separatory funnel of similar capacity, as suggested in a foot-note in my original paper. In my experience, the use of this later form of reductor repeatedly gave duplicate results which were, coincident to the fourth decimal place. R. W. RAYMOND, New York, N. Y.:-The. remarks of Mr. Jones recall to my mind an interesting part of the history of the Institute, and, of its relation to modern progress in the department covered by this interesting and valuable paper. In

Mar 1, 1906

Ninetecn papers and a round table. as follows: The Future of the American Iron and Steel Industry (Howe memorial Lecture), by Zay Jeffries; Rote of Carbon Elimination and Degree of Oxidation of metal Hath in Isasic Open-hearth Practice. 11, by ,Alexander L. Feild; A New Method for determining lron Oxide in Liquid Steel, by C. H. Herty. Jr., J. M. Gaines. Jr., H. Freeman and M. W. Lightner; I'racticsl Obarrvntions on Manufacture of basic Open-hearth, High-carbon Killed Steel, by W. J. Itcagan; Production of Gray lron from steel Scrap in the Electric Furnace, by T. F. Baily; reclaim ing Steel-foundry Sanda, by A. H. Dierker; Influence of Rate of Cooling on Dendritic Structure and Microstructure of Some Hypocutectoid Steel, by Albert Sauveur and C. H. Chou; Transformation of Austcnite at Constant Subcritiral Temprratures, by I?. S. Dnvenport and E. C. Bain; Progress Notes on the Iron-silicon Equilibrium Diagram, by Bradley stoughton and S. Greiner; Influence of Nitrogen on Special Steels and Some Experiments on Case-hardening with Nitrogen; by Shun-ichi Satoh; Production and Some properties of Large Iron Crystals, by N. A. Ziegler: Tensile Properties of Rail and Other Steels at Elevated Temperatures, by John R. Freeman, Jr. and G. Willard Quick; Endurance Properties of Steel in Steam, by T. S. Fullcr; Development of Casing for Deep Wells; a Study of Structural Alloy Steels, by F. W. Bremmer; Electrolytic Iron from Sulfide Ores. by Robert D. Pike, George H. West, L. V. Steek, Ross Cummings and B. P. Littlc; Sintering Limonitic Iron Ores at Ironton, Minnesota, by Perry G. Harrison; Concentration of the mesabi Ilematites, by E. W. Davia; Resistance of Iron Ores to Decrepitation and Mechanical Work, by T. L. Joseph and E. P. Barrett; Experiments Demonstrate Method of Producing Artificial Manganese Ore, by T. L. Joseph, E. P. Barrett and C. E. Wood; Iron Ore Round Table.

Jan 1, 1930

By W. Rostoker, H. Nichols

The embrittlement by mercury of aluminum alloys in various states of anneal, cold work, and aging has been studied. It is shown that single phase and non-precipitation hardened structures irrespective of de,pee of prior cold work demonstrate some small measure of yielding before fracture occurs. Sub-yield-stress failure is confined to the aged state, and embrittlement is accentuated by small plastic prestrains. With large plastic pyestrains, embrittle~nent is progressively reduced. In previous work' it was shown that the propensity of commercial aluminum alloys for embrittlement when wetted with mercury seems to be related primarily to the intrinsic strength in the normal un-wetted condition. The data from a large number of commercial alloys in various states of anneal, cold work, and/or aging gave a generalized relationship. At low strength levels, the wetted fracture strength increases proportionately to the increase in tensile strength; but above 65,000 psi normal ultimate strength, the trend is abruptly reversed, and the wetted fracture stress decreases proportionately to the increase in tensile strength. This paper will demonstrate that the simple character of this relationship between normal tensile strength and wetted fracture strength is fortuitous. It will be shown that structure and thermal-mechanical history are clearly relevant factors. The term brittle fracture has been used to connote the geometry of the fracture surface (transverse vs shear plane) or the negligible extent of preceding plastic strain. At its maximum effectiveness, liquid metal embrittlement can satisfy both criteria—fracture transverse to the axis of tension and without observable plastic strain. In this paper, brittle fracture will signify failure at stresses below the engi-

Jan 1, 1962