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By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By W. A. Backofen, R. L. Fleischer

Single crystal, bicrystal, and polycrystal tensile tests of aluminum at 4.2°K, 77°K, and 300°K have been used to examine the role of grain boundaries in the deformation process. Results indicate that a grain boundary may affect the extent and slope of easy glide. The stage II hardening rate, on the other hand, is independent of the presence or absence of grain boundaries. This conclusion allows the size of the region of multiple slip caused by an incompatible grain boundary to be determined. For the size of bicyystal sample used in this study, multiple slip occurs in about half of the cross section. PREVIOUS studies of the stress-strain characteristics of bicrystals of face-centered-cubic metals have been limited to aluminuml-5 at room temperature. Recent results, however, indicate that the stress-strain curves of single crystals of such metals may be separated into at least three stages6 in which different deformation processes are occurring7 provided testing is done at sufficiently low temperatures.' Since for aluminum a well-defined stage II develops only below room temperature, previous studies have not been able to relate effects of grain boundaries to all of the three stages of deformation. It is therefore to be expected that low-temperature deformation of aluminum single crystals and bicrystals should clarify the effects of grain boundaries on the different processes of deformation. EXPERIMENTAL PROCEDURE Single crystals and bicrystals were grown from the melt by the standard techniqueg with aluminum reported by Alcoa to be 99.993 pct pure. Ridges in the boat were used to guide the grain boundary during growth, assuring that the boundary would bisect the sample.10 The rate of furnace motion during growth was 1.0 cm per hr. During growth zone purification resulted, as evidenced by the ability of the first material to freeze to recrystallize at room temperature following severe deformation. Samples were approximately 4.4 X 6.6 mm in cross section and 103.5 mm in length between grips. Samples were annealed at 635" i 5°C for 40 hr and furnace cooled over a 7-hr period. They were then electropolished in a solution of 5 parts methanol to 1 part perchloric acid at a current density of 15 amp per sq dm for about 30 min at temperatures below 0°C. Tensile testing was performed at 295" (room temperature), 77" (sample in liquid nitrogen), and 4.2"K (sample in liquid helium) on the hard-type machine indicated schematically in Fig. 1. The machine con- sists basically of a tube surrounding a rod; one end of the sample is attached to each member, and the rod is pulled up the tube to extend the sample. The rod is rigidly mounted and is moved vertically by a system described by asinski." The pulling force is measured continuously by an electrical strain gage load cell, and the relative displacement of the tube and rod is also recorded continuously by a soft cantilever beam with electrical strain gages. Maximum stress and strain sensitivities were ±2g per sq mm and * 3-10-5. In all tests the strain rate was approximately 5.10-5 per sec. The thin wires in the tensile apparatus introduce softness, which may be corrected for, however, by measuring load vs displacement with the sample replaced by an elastic member. For loads greater than 15 kg the spring constant is 1.875.106 g per cm. The flexible wires also served to reduce substantially the large shearing forces which may arise in the case of grips having horizontal rigidity.'' As in any gripping system, however, bending moments will arise in the course of deformation by single slip. Engineering stress, s = (load)/(original cross-sectional area), and strain, E = (increase in length)/ (original length), are used for stress-strain curves unless otherwise indicated. Tables list resolved shear stress, T=mo and shear strain ? = dm, where m is the usual Schmid resolved shear stress factor for the primary slip system at the start of deformation. The first group of samples to be described forms an isoaxial set, all of the crystals making up the single crystals or bicrystals having the same tensile axis, the orientation of which is indicated by the cross in Fig. 2. For this orientation the primary slip plane and slip direction make angles of 45 deg with the tensile axis and the Schmid factor m has its maximum possible value of 0.5. Rotations about the tensile axis are indexed by means of an angle 0 between the small-area surface of the samples and the projection of the primary slip direction onto the cross section, as defined in Fig. 3. In single crystals, values of 0 were 0 and 90 deg, while in bicrystals 0 values were (0 deg, 180 deg), (90 deg, 270 deg), and (0 deg, 90 deg) as indicated in Fig. 4.

Jan 1, 1961

By James W. Dally, William L. Fourney, Anders Ladegaard Peterson

For the past 3 years, the authors have been conducting research sponsored by the National Science Foundation (RANN) to improve the process of excavation by drilling and blasting. The approach followed has been experimental where the development of stress waves and fractures initiated at the bore hole have been investigated in order to obtain a complete understanding of the dynamic fracture process. The second step in the approach has been to introduce modifications in the drill and blast procedure which will permit closer control of the fracture process. The laboratory investigations involve high speed photography where the dynamic fracture process is recorded with a Cranz-Schardin 1, 2 multiple-spark camera. The camera is equipped with 16 spark gaps which are pulsed at 25 K volts to produce an intense but very short (0.5 sec) flash of light. The camera is capable of recording 16 photographs of a dynamic event at framing rates which can be varied from 30,000 to 1,500,000 frames per second. The exposure time is sufficiently short to stop motion associated with detonating explosive charges and to make visible the details of the fracture process at a bore hose. The bore hole in a massive intact rock formation is modelled with a two dimensional plate containing a circular hole to represent the bore hole. The model material employed is a transparent polyester known commercially as Homalite 100.* This polymeric material is extremely brittle as evidenced by its extremely low fracture toughness of [ ]. The fracture toughness is a measure of the ability of a material to resist the propagation of flaws or small cracks. In comparison, Schmidt3 has recently measured the fracture toughness of Salem limestone and determined [ ]. Thus, the Homalite 100 should closely model the brittle nature of rock where fractures occur at small flaws and propagate without any apparent plastic deformation. Homalite 100 is also birefringent, which indicates that it becomes optically anisotropic when subjected to either static or dynamic loads. Circularly polarized light is transmitted through the loaded Homalite 100 model in a polariscope4 and the birefringence produces an optical interference pattern which is called a fringe pattern. For dynamic photoelasticity, the multiple-spark camera is equipped with polaroid filters to produce the circularly polarized light required to generate the photoelastic fringe patterns. An example of a singlespark frame showing a fringe pattern from a typical experiment is presented in [Fig. 1]. The photograph was taken 0.000072 sec (72 sec) after the detonation of the explosive charge. The circular fringes are due to the outgoing dilatational or P type stress wave and travel with a velocity of 85,000 in. per sec (2260 m/sec) in the Homalite 100. The P wave is followed by a second lower velocity stress wave known as the shear or S type wave which propagates at a velocity of 49,000 in. per sec (1245 m/sec). In the local neighborhood of the bore hole, several radial cracks are visible. These cracks propagate at essentially a constant velocity of 15,000 in. per sec (380 m/sec) prior to arrest. The fringes about the crack tips and in the local region of the bore hole are primarily due to the residual gases contained in the bore hole after the explosive charge was detonated. Sixteen frames similar to this one are recorded during the experiment to give full field visualization of the dynamic event at 16 discrete times over its duration. The fringe order number N is related to the difference in the principal stresses of and 02 according to a stress optic law4: [ ] where f0 = material fringe value, and h = model thickness. The wholefield dynamic-fringe patterns provide a basis for simultaneously observing the interaction between propagating cracks and the stresses which drive these cracks. Fracture Control Experiments Improvements in the efficiency of the drill and blast procedures must involve close control of the fracture process following the detonation of an explosive charge in a bore hole. By control it is implied that the number of cracks initiated and the location of each crack on the wall of the bore hole can be specified. Control also, involves orienting each crack and maintaining the crack path and velocity until the specified crack length is achieved. If the entire fracture process can be controlled, then rounds can be designed to optimize volume removed. fragment size and minimize costs. One area of blasting where fracture control is vitally important is in underground excavation where the strength and stability of the rock walls must be maintained and smoothness and precision of the walls must be achieved. The smooth blasting method is one of the most commonly employed procedures for achieving some degree of fracture control. In smooth blasting, the central region of material is first removed, and then the final row of closely spaced undercharged or cushioned holes are fired to remove the final volume and produce a smooth wall. In some instances, unloaded or dummy holes between the loaded holes are recommended to guide the fracture plane. This investigation pertained to an evaluation of 3 features of the smooth blasting process. These included (a) the effect of stress reinforcement on fracture by simultaneously firing 2 charges; (b) the influence of a dummy hole on control of the fracture planes between 2 simultaneously fired charge holes; and (c) the influence of dummy hole spacing on fracture plane control.

Jan 1, 1979

By B. A. Wilcox, A. H. Clauer

The steady-state creep of TD Nickel NL + 2 001 pct TltOz) has been studied orer the telirperatve range 325&apos; to 1100O and the stress range 15,000 to 36,000 psi. At high temperatures (aboue 0.5 T& gran-boundary slzding is the )nost znportant )node of creep deformation, and the steady-state creep rate, is, can be related to stress and temperature by: where Q = 190 kcal pev mole and n has an unusually high value of 40. A creep mechanism based on cross slip of dislocations around The O2 particles can satisfactovily explain the low-temperature (T < 0.5 T,) cveep behavior, and the follo wing relation is applicable: Q, (a) is found to decrease from 57 to 46 kcal per mole as the stress is increased from 32,000 to 36,000 psi. THERE have been a variety of theories proposed to explain the influence of dispersed second-phase particles on the yield strength and flow stress of metals, and these have been reviewed recently by Kelly and icholson.&apos; However, only several attempts2"4 have been made to develop mechanistic treatments which characterize the creep behavior of dispersion-strengthened metals, and to date these have not been fully evaluated experimentally. weertman2 and Ansell and weertman3 proposed a quantitative creep theory for coarse-grairzed dispersion-strengthened metals, based on the concept that the rate-controlling process for steady-state creep was the climb of dislocations over second-phase particles, as suggested by choeck. The theory predicted that the steady-state creep rate, <,, was proportional to the applied stress, a, for low stresses and that is a4 o for high stresses. The activation energy for creep, Q,, was equivalent to that for self-diffusion, Qs.d., in the matrix. Some limited experimental evidence in support of this theory was obtained on a recrystallized Al-Alz03 S.A.P.-type alloy by Ansell and Lenel.6 Ansell and weertman3 also developed a semiquanti-tative theory for high-temperature creep of lineg-rained dispersion-strengthened metals in order to explain their results on an extruded S:A.P.-type alloy, which had a fine-grained fibrous structure. They suggested that the rate of dislocation generation from grain boundaries was the rate-controlling process, and fitted their results to the equation: where Q, was found to be 150 kcal per mole, i.e., QC- 4Q,.d. in aluminum. Similar high activation energies for creep7-&apos;&apos; and tensile deformation" of dispersion-strengthened alloys have been observed by other investigators for S.A.P.,&apos;" indium-glass bead omosites, and Ni + A1203 alls.&apos; There is no general agreement regarding the mechanisms involved in the creep of dispersion-strengthened metals, and this is due in part to the lack of detailed studies relating the structures of crept specimens to the mechanical behavior. The present investigation on thoriated nickel was undertaken with the aim of studying the structural changes which occur during creep of a dispersion-strengthened alloy and rationalizing the observed mechanical behavior in terms of the creep structures. EXPERIMENTAL METHODS The material used in this investigation was 1/2-in.-diam TD Nickel bar, which contained 2.3 vol pct Tho,. Obtained from E. I. duPont de Nemours & Co., Inc. The final fabrication treatment by DuPont consisted of -95 pct reduction by swaging followed by a 1-hr anneal at 1000°C. Transmission and replica electron microscopy revealed that the material had a fine-grained fibered structure with an average transverse grain size of -1 p and a longitudinal grain size of 10 to 15 p. Selected-area diffraction indicated that the fiber axis was parallel to (OOl), in agreement with the results of Inman eta1." All creep specimens were vacuum-annealed at 1300°C for 3 hr prior to testing. Transmission electron microscopy showed that the only structural change due to annealing was a slight decrease in dislocation density, confirming the reported high degree of structural stability.13 Furthermore, recrys-tallization or grain growth during creep was never observed. The structure typical of uncrept material (after the 1300 C, 3-hr anneal) is shown in Fig. 1. The grain boundaries are predominantly high angle and. although some areas show a tangled cell structure, the grain interiors are relatively dislocation-free. Individual dislocations are strongly pinned by the Tho2 particles; i.e., very rarely did dislocations move within a thin foil. The grey "halos" around some of the larger particles which protrude out of the foil surface arise from contamination in the electron microscoge. The Tho, particle size ranged from -100 to IOOOA, and the distribution is shown in Fig. 2. The technique used to obtain the data in Fig. 2 consisted of dissolving the nickel matrix in acid, collecting the Tho2 particles on cellulose acetate, and measuring about 1000 particle diameters in the electron microscope. Similar results were obtained by measuring about 600 particles in thin foils, an; the average particle size was found to be 2r, = 370A. Using the data in Fig. 2 (annealed structure), the mean planar center-to-center particle

Jan 1, 1967

There were two official representatives of Foreign Governments as guests at the Chicago Meeting. One was Frederick Goransson, managing director of the Saudvikens Steel Works, who represented the Jernkonteret, the Iron and Steel In-stitute of Sweden, and who came to this country especially for our meeting. The other distinguished guest was Commander Toublet, who repre-sented the French Embassy. Commander Toublet delivered a most polished address at the Banquet, dealing with the felicitous relations existing between this country and France for the last 150 years. Com-mander Toublet was accompanied by Mrs. Toublet, who won the hearts of all the ladies present, whose guest she was.

Jan 11, 1919

By Y. C. Liu, R. H. Richman

The effects of gel,manium and tin on the deformation and 9-e-crystallization textures of copper have been explored in detail with in the copper-rich terminal solid solutions. Addition of solute to copper produces a change in deformation texture from the copper type to the 70 :30 brass type. This transition has been measured quantitatively The types mid proportions of recrystal-lization components have been determined as a function of com-position, and correlation of recrystallization components with specific deformation components is discussed. On the basis of information available in the literature, it has been suggested that the effect of solute elements on the recrystallization texture of copper

Jan 1, 1961

By John F. Lundeberg

CLAUSS1 observed that if isothermal creep data could be approximated as straight lines on a log stress-log time plot, a relationship existed that could be expressed as log t = m log s + b [ l] where t = time,

Jan 1, 1965

By Arthur Phillips, R. M. Brick, A. J. Smith

A previous publication1§ has described the effect of quenching stresses on the lattice parameter values of high-purity aluminum-copper alloys particularly with reference to the solution and precipitation of CuAl². A similar study has been made of the aluminum-rich aluminum-magnesium alloys. Attention has been directed in the present investigation to the magnitude of the quenching stresses as affected by the specimen size and shape, the number of solute atoms and the quenching rate. The effect of cooling stresses in causing plastic defomation or cracking has been considered in relation to the physical properties of the alloy On reheating alloys in the two-phase field, the time required for precipitation to occur has been observed in connection with the degrec of supersaturation, the rate of diffusion of the solute atoms as a function of the comparative atomic radii, degree of strain, temperature of reheating and grain size. A few qualitative comparisons on the relative effect of these factors have been drawn between the aluminum-copper alloys and the aluminum-magnesium alloys. Strain in Solid-solution Alloys A 10 per cent magnesium alloy ill the form of chill-cast bars was furnished by the Aluminum Company of America through the courtesy of L. W. Kempf. Additional alloys were prepared using alllminum (99.95 per cent Al) and high-grade magnesium. The alloys listed in Table 1 were melted in an Acheson graphite crucible under a flux of fused MgCl², CaC12, NaCI. Chill-cast rods were sealed under vacuum in Pyrex glass, homogenized several days at 450&apos; C., air-cooled and machined to rods of from 1/8 to ¾-in. dia. Metal powders taken from these rods with a fine-toothed saw were again sealed under vacuum in

Jan 1, 1935

By R. M. Brick, Arthur Phillips, A. J. Smith

A previous publication1§ has described the effect of quenching stresses on the lattice parameter values of high-purity aluminum-copper alloys particularly with reference to the solution and precipitation of CuAl². A similar study has been made of the aluminum-rich aluminum-magnesium alloys. Attention has been directed in the present investigation to the magnitude of the quenching stresses as affected by the specimen size and shape, the number of solute atoms and the quenching rate. The effect of cooling stresses in causing plastic defomation or cracking has been considered in relation to the physical properties of the alloy On reheating alloys in the two-phase field, the time required for precipitation to occur has been observed in connection with the degrec of supersaturation, the rate of diffusion of the solute atoms as a function of the comparative atomic radii, degree of strain, temperature of reheating and grain size. A few qualitative comparisons on the relative effect of these factors have been drawn between the aluminum-copper alloys and the aluminum-magnesium alloys. Strain in Solid-solution Alloys A 10 per cent magnesium alloy ill the form of chill-cast bars was furnished by the Aluminum Company of America through the courtesy of L. W. Kempf. Additional alloys were prepared using alllminum (99.95 per cent Al) and high-grade magnesium. The alloys listed in Table 1 were melted in an Acheson graphite crucible under a flux of fused MgCl², CaC12, NaCI. Chill-cast rods were sealed under vacuum in Pyrex glass, homogenized several days at 450&apos; C., air-cooled and machined to rods of from 1/8 to ¾-in. dia. Metal powders taken from these rods with a fine-toothed saw were again sealed under vacuum in

Jan 1, 1935

By J. W. Pugh, Sam Leber

Single crystals of tungsten were made and deformed in tension at 3000°C. The slip traces so formed on these crystals were analysed to determine the apparent slip system. Results indicate that deformation occurs in the<III> direction on planes of maximum shear stress. This determination agrees with the early work of Taylor and Elam on other body-centered cubic crystals at lout temperatures. SLIP in face-centered cubic and hexagonal close-packed metals has consistently manifested itself in straight traces which indicate that glide takes place on planes of highest atomic density and in directions of closest packing. The slip traces observed on body-centered cubic metals are, on the other hand, frequently branched and wavy, and indicate that while glide takes place in the direction of closest packing, it does not necessarily choose the plane of highest density. The early work of Taylor and Elam1 4 indicated that glide took place in the close-packed direction on planes close to those defined by the maximum shear stress. Subsequent investigations have tried to rationalize these observations in terms of an elementary process on the close-packed planes (110). For example, Elam5 and Grenin~er&apos; have suggested alternate glide on nonparallel (110) planes with the observed result that the summation of these glides results in a trace which defines some plane other than{110). Madden and chen7 have recently reviewed the phenomenological and theoretical aspects of noncrystallographic slip. More recently Koehler&apos; has presented a model of dislocation propagation which permits another rationalization. He indicated that dislocation loops are transferred from one glide plane to another by double cross-slip of screw segments. It is reasonable to assume that, on the average, such transfers may result in a trace which approaches the plane of maximum shear stress. The work described in this paper will show that

Jan 1, 1961

By H. l. Burghoff, A. I. Blank

J. J. Kanter.*—The authors of this paper have demonstrated that at 500°F their alloy will elongate, under appropriately adjusted stress, one or two per cent over a period of 6000 hr. Then they show that after the alloy has so elongated, it will still elongate anothcr 40 per cent if it is tested at ordinary temperature. I should like to ask the authors how much more than 2 per cent over a period of 6000 hr. their alloy will elongate at 500°F. H. L. BuRghofE.—We do not know, because we have not carried out stress-rupture tests on this material. I believe your point concerning the desirability of stress-rupture testing is very well taken. In the material that we have subsequently tested we have not seen any signs of deterioration. We do not know how much further it is possible to go beyond the 2 per cent before finding grain-boundary separation. We have not encountered any under the conditions of the test. W. E. Kingston.†—IS this particular type of copper susceptible to strain-aging, and if so at those comparatively low temperatures, is that going to affect the shape of the curve? By strain-aging I mean the phenomena that certain ferrous alloys show in which the resistance to deformation increases suddenly during the low-temperature creep cycle, apparently due to some precipitation type of reaction, perhaps analogous to hydrogen embrittlement. H. L. BUrghoff.—I believe that this material is not subject to strain-aging of this type. It is very high in copper content, of course, nearly loo per cent. There are some very minor impurities and it carries a small amount of phosphorus, which, unless it is present as an oxide, should be in solid solution well within the solubility limits. I believe it does not precipitate

Jan 1, 1945

By A. N. Mitinsky

(San Francisco Meeting, September, 1915) THE theory of elasticity, the science of the strength of materials, and all our calculations regarding engineering structures are based on Hooke&apos;s law, that in loaded bodies the deformations are, proportional to the load producing them. Without this law it would be impossible to design intelligently engineering structures such as bridges, frames, axles, etc. This being the case, the proportional limit,1 that is, the point at which deformation ceases to be proportional to load, is the most important factor in engineering design. Further, the working fiber stress should be fixed in reference to the proportional limit instead of, as is usual, in reference to the ultimate strength. The incorrect use of the ultimate strength instead of the proportional limit in setting the working fiber stress is probably clue to two reasons: (1) it is a more delicate operation to measure the proportional limit; (2) it is usually -assumed, though incorrectly, that the proportional limit is determined by the ultimate -strength. In Germany the point at which permanent set first appears is often taken instead of the proportional limit. The two points will coincide if Gerstner&apos;s law, that elastic deformations are proportional to the loads producing them both before and after permanent set, is true; and the limit of proportionality and the elastic limit or point of permanent set will both &apos;be represented on a stress-strain diagram, by the point at which the line ceases to be a straight line and becomes curved-or changes its inclination. It is to be further noted that the difference in definition between proportional limit and elastic limit introduces a difference in methods of determination in the testing laboratory. The German method of determining. the elastic limit by alternately loading and unloading

Jan 8, 1915

By S. R. Maloof

In 1945, Hollomon&apos; showed that after plastic yielding and prior to necking under simple tension, both ferrous and nonferrous materials are approximated by an equation of the following form: where, a = true stress K = strength coefficient 5 = true strain n = strain hardening exponent If a material is stress free, a plot of log o vs log 6 would be expected to be a straight line, the slope of which is the strain-hardening exponent (n) and the intercept on the ordinate axis for 6 = 1. is the logarithm of the strength coefficient K. It can be easily shown that the strain-hardening exponent in the above equation is equal to the total uniform elongation prior to necking. Thus, one can determine the total uniform elongation prior to necking from such a plot and, as pointed out by C. W. MacGregor, 2 it is the amount of strain prior to necking which determines the extent to which a material may be deep drawn. In the view of the current interest in the fabrication of beryllium shapes, it was thought that a knowledge of the strain-hardening exponent of cross-rolled beryllium sheet would be of general interest. Load-strain data after yielding and prior to necking was taken from the work of Greenspan,3 converted to true stress and true-plastic strain, and plotted on log-log paper as shown in Fig. 1. The value of Young&apos;s modulus E for beryllium was taken as 43 . l06 psi. The slope of this plot gave a value of 0.212 for the strain-hardening exponent (n) and the intercept on the ordinate axis a value of 105,000 for K. The total uniform elongation is thus 21.2 pct, in excellent agreement with the value estimated by Greenspan (about 20 pct). Furthermore,

Jan 1, 1960

By K. Heindlhofer

ESTIMATES of the "plasticity" of a metal are commonly deduced from three types of test-tensile, torsion and impact. The several results have been more or less at variance, though this disparity has attracted little notice, largely perhaps because they have been expressed in different terms. The discrepancy between the results of the three tests becomes obvious when each is made at a series of low temperatures, for the temperature range within which the "plasticity" of iron largely disappears proves to be very different in the three types of test. The rather abrupt disappearance of "plasticity" of iron within a narrow temperature range cannot be due to any physicochemical change (such as a precipitation) taking place in the material at that time, because the original plasticity is immediately regained when the temperature of the material is brought above the sensitive range. Accordingly this differ-ence in behavior shows that the "plasticity" of a metal depends upon the mode of action of the stresses which produce the deformation, and there-fore upon the method of test. Analysis of the stresses leads to the conclusion that the observed plasticity of a metal is determined by the relation between its resistance to rupture by separation and its resistance to shear (slip), on the one hand, and between the effective normal and shearing stresses on the other; and that the relation between the two resistances does not in general remain constant with change of temperature, and may somehow be altered to some extent by the previous treatment of the specimen. This suggests the view that the results of none of the usual mechanical tests are directly comparable even for a single metal tested at a series of tem-peratures, or for a series of metals at one temperature, because the propor-tion of the total resistance of the metal to the test contributed by the

Jan 1, 1934

By Fred Leighton, Wilson Blake

The microseismic method of detecting instability and high-stress zones in underground mines was developed by the U.S. Bureau of Mines (USBM) in the early 1940&apos;s.l,2 For about 25 years this method has been used throughout the world by mining and construction companies in assessing the stability of underground and surface excavations. Rock noises are the release of small amounts of stored strain energy propagating outward from their source as a seismic wave that can be detected with special geophysical equipment. This release of strain energy is caused by a rock mass undergoing load changes resulting in small-scale displacement adjustments such as microcracking, shearing, sliding, and crushing of crystal grains, some even as small as the elastic displacements themselves. No detailed field studies of any of these mechanisms have been made, and knowledge about the origin of rock noises is relatively incomplete. Laboratory tests have shown that when rocks are stressed in a testing machine, the rock noise rate-the number of rock noises generated per unit of time increases with increasing applied stress.3 This increase is most pronounced as the ultimate strength of the rock is approached. The standard field procedure has been to monitor a rock structure at intervals and plot rock noise rates vs. time, thus gaining a semiquantitative estimate of the behavior and stability of the structure. The success of such monitoring, however, has depended almost entirely on the experience and knowledge of the operator, his interpretation of the data, and his equipment. Very little study has been devoted to the basic properties of the vibration record of a rock noise. USBM decided that the microseismic method was being used sufficiently by various mining and construction companies

Jan 1, 1970

By Norbert R. Morgenstern

INTRODUCTION An understanding of the role of water in controlling the stability of rock masses is central for a rational approach to the subject. The presence of water can hinder mining opera- tions in two ways: 1. excessive discharge 2. excessive pressure It should be noted that if the rock mass is very tight, excessive pressures can exist without large discharges. Alternatively, if abundant water is available and the rock mass is open, then substantial discharges can occur under quite small pressures. The problems associated with excessive discharge are usually well understood by the mining engineer. Vehicle mobility is inhibited, some areas are flooded and hence become inaccessible; at best, a costly nuisance exists. The methods of solving these problems are also well-known to mining engineers. They generally involve tapping the source of the excessive discharge and channeling it away in such a manner that any hindrance to the mining operation is minimized. The effects of water pressure on the stability of rock masses are less obvious and the following will be devoted solely to this aspect of the problem. The manner in which water pressures enter into the consideration of stability is made clear by an understanding of the concept of effective stress. THE CONCEPT OF EFFECTIVE STRESS The simplest mechanical model for the problem of rock slope stability consists of a rough, rigid block sliding down an inclined plane under the influence of gravity. This is illustrated in [Fig. 1]. The down-slope component of the weight of the block tends to produce movement which is resisted by the shearing force generated by friction along the base of the block. The shear stress per unit area inducing movement is

Jan 1, 1971

By K. Thirumalai

Although the term "spalling" has long been known, Norton l first referred to its usage for the fracture or disintegration of materials subjected to rapid temperature changes. Spalling of ceramic materials at high temperatures has received attention in the past.2-4 Removal of the char formed during ablation in reentry of space vehicles has been referred to as mechanical spalling.5 The first experiments to evaluate the process of rock fragmentation by thermal spalling were conducted by Stoces6 using a series of gasoline burners on the quartz veins of the Zinnwald deep mines in Germany. After the development of rocket-jet burners, the principles of thermal spalling combined with high fluid momentum found wide practical application in rocks. The well-known jet piercing process for drilling blastholes in taconite and for jet channeling in the quarrying of granite are among the more notable of these application.7 For the purposes of this study, thermal spalling or spallation of rocks is defined as progressive failure caused by thermal stresses induced by a sudden application of heat from a high temperature heat source. Gray observes that the size of the spall is dependent on the pattern of induced thermal stresses before failure. The spallability or the relative susceptibility of rocks to failure by thermal spalling is a complex but potentially useful parameter for qualitative comparisons. Fundamental differences exist in the degree of spallability among different types of rocks. Accurate prediction of spallability of any particular rock has so far not been possible. Measurement of the state of stress and temperature in the rock during the rapid thermal spalling process poses difficult problems that must be solved. Identifying the parameters that influence the thermal spalling proc-

Jan 1, 1970

By William G. Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the nonhomogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of deforming beyond the limit of purely elastic strains, a plasticity theory is required. The purpose of this chapter is to present a plasticity theory for anisotropic rocks and soils. The proposed theory is based on the work of Hill in anisotropic metal plasticity and represents an extension of his work so as to include anisotropic geologic materials. The point of departure from metal plasticity theory begins with the inclusion of the normal stresses as linear terms in the yield condition, which plays a central role in plasticity. Once the yield condition is established, the plastic strain increments are obtained immediately through the principle of normality. For practical applications, some simplification of the three-dimensional theory is re-

Jan 1, 1972

By W. F. Carew, F. A. Crossley

The stress for rupture in 500 hr at 1000° F has been reported to be about 13,000 psi higher for Widmanstitten than for equiaxed microstructures for the Ti-7A1-3Mo alloy.1,2 Also, limited data indicated Widmanstatten and equiaxed micro-structures to have approximately the same creep resistance at 1000°F.&apos; Recently, data have been obtained which show Widmanstatten structures to be significantly more creep resistant than equiaxed structures at 1000°F, see Fig. 1. These data represent several ingots and several heat treatments of the solution treat and age type. The thermal history and tensile properties corresponding to the creep data are given in Table I. The creep data were taken from creep-rupture tests. The associ- ated rupture data are given in Table 11. It may be noted that total creep deformations are considerably greater for equiaxed structures. Previous evaluations of stability indicated that all of the structures tested are stable with respect to exposure to stress at elevated temperature.1,2 For a minimum creep rate of 10-4 in. per in. per hr the difference in stress levels is indicated to be about 17,000 psi. Holden,et found an irreversible contraction upon heating three a-ß titanium alloys in the equiaxed condition above their ß-transus temperatures. The alloys were: Ti-6Al-4V, Ti-155 A (5Al-1.3Cr-1.5Fe-1.2Mo), and C-130 AM (44-4Mn). The net contractions in length between the original equiaxed and the final Widmanstatten structures measured at room temperature were: 0.4, 0.4, and 0.7 pct, respectively. The greater creep and rupture resistance of the WidmanstStten structure of the Ti-7Al-3Mo alloy may be associated with the phenomenon

Jan 1, 1959

By P. W. Ramsey, D. P. Kedzie

INCREASING demand for improved strength-weight ratios made on aircraft structures has resulted in a gradual increase in the tensile strength requirements for steels used in such applications. As the cyclic loads often are more critical than static loads, and the fatigue properties are generally the design criteria, the question arises as to whether an improvement in fatigue properties accompanies the increased tensile strength. The present investigation was undertaken to determine the relationship between fatigue and tensile properties for an aircraft quality steel in the 155 to 280 ksi (1000 psi) tensile strength range, using the Prot method of fatigue testing. Procedure and Results After preliminary work to establish proper heat treating procedures for this heat of aircraft quality electric furnace steel (a Ni-Cr-Mo-V steel," AMS- Prot Fatigue Testing Method—The determination of the endurance limit by the conventional Wohler method can be time-consuming and easily require 20 specimens when statistical variance is to be established. This is also true when endurance limit loads are determined on actual parts or subassem-blies, and the desirability of a reliable accelerated method has been evident for some time. The primary advantage of the Prot method of fatigue testing is in reducing the number of specimens and the time required for each test. Unlike the Wohler method, every Prot specimen tested con- tributes to the determination of the endurance limit, and the authors have been able to duplicate Wohler results obtained with 20 specimens with only half the specimens and a fourth of the total cycles. This new technique for defining the endurance limit was proposed in 1948&apos; by Marcel Prot and consists of progressively increasing cyclic stress until fatigue failure occurs. By varying the load rate, a, a useful relationship is found to exist with failure stress, so that for steel the failure stress appears to

Jan 1, 1958