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By K. U. Snowden, J. N. Greenwood

CRACKS which form in lead exposed to fluctuating stress frequently follow a rectangular pattern. It is well known that under ordinary atmospheric conditions these cracks are intercrystalline. On the other hand after fabrication the crystal grains in lead are in general irregular polygons. The observed facts appear to be mutually contradictory. Re-examination of some lead failures has confirmed that the rectangular cracks are intercrystal- line. It follows therefore that under fluctuating stress some of the grains lose their irregular outlines and become approximately regular polygons of cubic type. G. R. Gohn and W. C. Ellis* suggest that this is due to recrystallization during the life of the part, in such a way that the new grain boundaries are aligned at 45 deg to the longitudinal strain prior to the formation of the fatigue crack. Experiments at Baillieu Laboratory—Some recent experiments carried out in the Baillieu Laboratory in conjunction with the Broken Hill Associated Smelters have thrown some light on this transition. A test piece of pure lead was polished chemically

Jan 1, 1959

By D. Krammer, E. S. Machlin

The effect of a brior high-temperature creep strain on the low-temperature ductility of commercially pure nickel has been evaluated. The low-temperature (-196°C) ductility decreases linearly with an increase in prior high-temperature (920°C) creep strain. The effect is experimentally correlated to the formation of inter crystalline cracks and voids during the prior high-temperature creep strain. The magnitude of the effect is also believed to be a function of the notch sensitivity of the material. SEVERAL mechanisms have been presented to explain the process of inter crystalline cracking in metals undergoing high-temperature creep. zenerl has suggested that grain boundary relaxation of shear stresses could build up high stresses at ob- stacles to grain boundary shear and thereby nucleate a crack. Chang and rant' have experimentally demonstrated that cracks do form at obstacles to grain boundary shear such as lines where three grains meet. The role of vacancies in the mechanism of high-temperature inter crystalline cracking has been explored by Machlt with the conclusion that the nu-cleation of voids by vacancy condensation is almost

Jan 1, 1960

By Nicholas J. Grant, H. C. Chang

Microscopic observations during creep tests were made on AI-20 pet Zn, 80 pet Ni-20 pet Cr, and 25 and 3S aluminum specimens. All these materials failed in an inter-crystalline manner under certain stress and temperature conditions. Particular atten-tion was given to the initiation and propagation of intercrystalline cracks in coarsegrained AI-20 pct Zn specimens. The geometry of the grains and grain boundaries in these specimens was known before the tests. On the basis of the observations and a knowledge of the interaction between grains and grain boundaries, a mechanism of intercrystalline fracture and propagation of the fracture has been proposed. METAL, and alloy fracture occurs essentially in two ways: transcrystalline and intemrystalline. In the past most of the work done in this field was centered on the determination of stress criteria for fracture. The specimens used for these studies were tested under varying conditions of stress state, temperature, and strain rate. Unfortunately, very little attention was given to the initiation and propagation of the fracture, whereas the nature of fracture was examined closely only after failure. Several extensive reviews of these studies have been published by Orowan, Smith, Barrett, and Petch.1, 4 It is well known that a material which exhibits a ductile and transcrystalline fracture can be made to exhibit a brittle and intercrystalline fracture by modifying its composition and by heat treatment. This modification may or may not result in microscopically observable precipitation in the grain boundaries." In the creep of any one alloy the transition of transcrystalline to intercrystalline fracture is a function of stress, strain rate, and temperature." The tendency for intercrystalline fracture to occur increases as the strain rate decreases and the testing temperature increases. Extensive work on high purity aluminum (99.995 pet) under creep conditions showed the importance of the interaction between grains and grain boundaries, and the different responses of grain and grain boundaries to the variables: stress, strain rate, and temperature.7, 8 It was also shown that grain boundary deformation necessarily has to be accommodated in the grains by various deformation means as. for example, fold formation. The type of fracture resulting from the creep of high purity aluminum was invariably found to be transcrystalline. On the other hand, 2S and 3s aluminum were, under certain conditions, found to fracture in an intercrystalline manner." One reason given for this was that the grains could accommodate to a lesser extent the deformation of the grain boundaries.19 It was decided to examine this line of reasoning in greater detail and to investigate the particular interactions between grains and grain boundaries that result in the incidence and progression of inter-ct,ystalline fracture. It is also the purpose of this paper to show where and how intercrystalline cracks start and how they propagate to result in fracture. Several alloys—Al-20 pct Zn, 80 pet Ni-20 pet Cr, 2S and 3s aluminum-— were used for this study, but attention was paid mainly to the behavior of an A1-20 pet Zn alloy, since its general creep behavior has been established." From the results of this study a mechanism of intercrystalline fracture is proposed. Experimental Procedure The experimental procedure was similar to that used in previous work and has been detailed elsewhere.' Two parallel flat surfaces were milled from an originally round specimen, giving a gage portion which was 1x0.09X0.17 in. Some round specimens, 1/4 in. round by 1 in., were also tested. The A1-20 pet Zn specimens. which were annealed at 1030°F for 24 hr, showed two to four grains across the width of the test bar, and most of the grains occupied the whole thickness of the specimenu. Before some of the specimens were subjected to creep, the grain arrangement was mapped out in a development drawing, Fig. 1. The initiation and

Jan 1, 1957

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e'i; ei being parallel to the Burgers vector b, and e'3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?'1,?'2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?'2s'11b'1—?'1s'12b'1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s'12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x'i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x'i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b'1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b'1s033 sin a- rn2b's33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

By I. R. Kramer, H. Shen, S. E. Podlaseck

The tensile and creep properties of aluminum in vacuum have been investigated. It was found that the general effect of a vacuum environment was to reduce the rate of work hardening. Results obtained from creep tests showed that lowering the test pressure from 2 x 10-4 to 10-7 torr produced a decrease in the activation energy as much as 500 cal per mole. An attempt is made to explain these effects in terms of how the surface-stress field of a specimen may be affected by a vacuum environment during plastic deformation. In a previous paper,' the results were reported of some of our early work on the effect of vacuum environment on the stress-strain curve of aluminum single crystals. This effort has been extended to the studies of the tensile and creep properties in vacuum as a function of various metallurgical parameters. Some of the recent surface-effect studies2'3 have revealed that a region of high dislocation density, the so-called "debris" layer, is formed near the surface of the specimen as a result of plastic deformation. This layer acts as a surface barrier to oppose dislocation movement. The strength of this barrier depends on the surface condition such as oxidation or surface removal. Experimental results obtained from surface-removal work2, 3 indicate that such a surface barrier, which may be characterized by a stress field, affects the applied stress and the rate of work hardening. In the case of aluminum, this stress field was found to be directly proportional to the strain and the strain rate; however, the slope of this curve is independent of orientation of the crystal and may be altered by using different surface treatment. Since the escape of dislocations may be retarded by the presence of an oxide on the surface of a specimen, it is expected that a change in the rate of oxidation in vacuum will affect the process of dislocation accumulation in the debris layer. Consequently, it also affects the plastic behavior of a metal. This paper reports the changes in some of the creep and tensile properties of aluminum in vacuum and discussions of the observed effects in terms of the concept of the "debris" layer. EXPERIMENTAL PROCEDURE Tensile Tests. A sketch of the tensile apparatus is given in Fig. 1. This apparatus was contained in a bell jar (14 in. diam by 24 in. high) connected to a 10-in. vacuum system. The load was applied to the specimen by means of a gear train which was driven by a magnetic clutch located outside the vacuum chamber. The specimen, held by a pair of square shoulder grips, was attached to the load cell at the top and the drive gear at the bottom. A displacement transducer was placed between the two grips as shown in the figure to measure the elongation. Signals of elongation and load were amplified and recorded on an X-Y recorder. The system was capable of detecting loads as small as 0.025 lb and displacements of 0.0002 in. Shoulder-grip specimens of aluminum single crystals, having a nominal square cross section of 1/8 by 1/8 in. and a 3-1/2-in, gage length, were grown by the Bridgeman techniques. The original purity was 99.997 pet. The orientations of the crystals investigated are shown in Fig. 4(a). The crystals were annealed at 600°C for 2-1/2 hr, electropolished, and placed in the vacuum test chamber without any delay. All the crystals were deformed at a strain rate of 4 x 10-5 sec-1 at 24o ± 3°C. A study was made to find whether a chemically passive surface film would give the same effect as a vacuum environment. Specimens of aluminum 1100 (0.187 in. diam with a grain size of 0.1 mm)

Jan 1, 1965

By R. G. Garlick, H. B. Probst

Tungsten single-crystal specimens of various orientations were deformed in tension at room temperature. Slip traces indicated both (112)(111) and (110) (111) slip; however, about 10 pct plastic dejormation was required bejore these traces could he seen. Resolzled shear-stress considerations indicated that at least some of the particular systems observed were not those on which slip initiated hut were secondary systems. This is highly probable, considering the high plastic strains involved. Analysis of the stress data with respect to possible slip systems indicated that slip must have been initiated at stresses below the proportional-limit stresses measured. ALTHOUGH there is general agreement that slip deformation in fcc and hep metals takes place on the plane of close packing and in the direction of close packing, there is no such agreement for slip in bcc metals. It is generally agreed that the close-packed direction (111) is the slip direction, but investigations have led to conflicting descriptions of the slip plane. As Hoke and Maddin1 point out, there are essentially four points of view. 1) Deformation in bcc metals is composite shear on (112) and (110) planes or on nonparallel (110) planes, and any apparent slip on other planes can be accounted for completely by slip on these planes. Chen and Maddin have reported this to be the possible case for molybdenum." 2) Slip occurs in the (111) direction and is limited to {110), {112), and (123) planes (the three closest packed planes of the lattice). 3) Slip occurs in a (111) direction, but not necessarily on planes of close packing (banal slip). 4) Slip occurs in those directions and on those planes for which ß, the ratio of Burgers vector to interplanar spacing, is a minimum. The slip systems of the bcc metal tungsten have never been fully determined, although several investigators have reported pertinent results.3"7 The present work was initiated to determine the active slip systems in tungsten at room temperature, the critical resolved shear stresses associ- ated with these systems, and the orientation dependency of operative systems. These features of tungsten deformation at room temperature have never been reported in the literature. The authors find this somewhat surprising, particularly in view of the availability of tungsten single crystals since the advent of electron-beam zone-melting techniques and the widespread interest in refractory metals. It would seem apparent that such work has been attempted but the results have not been reported, possibly due to the conflict with deformation theory. The results of the present work conflict with any straightforward description of deformation based on the proposed explanations of slip in bcc metals. Although these conflicts have not been resolved, a presentation of the problem seems in order and should be of value to others working in this field. MATERIALS AND PROCEDURE Single-crystal tungsten rods of 1/8-in. diameter were grown from undoped commercial rod by one-pass electron-beam zone melting in apparatus previously described by witzke.8 Representative analyses of the rod before and after melting are given in Table I. There was no detectable zoning of impurities during melting. Buttonhead tensile specimens, as shown in Fig. 1, were machined from single crystals. Two flats 90 deg apart were ground in the gage length of each specimen. These flat surfaces facilitated the analysis of slip traces. No attempt was made to position these flats with respect to the crystal orientation. The worked surface layer of the machined specimens was removed by electrolytic polishing in a NaOH solution. Tensile-axis orientations were determined by standard Laue back-reflection techniques. The sharpness of the Laue spots indicated that the crystals were free of strain.

Jan 1, 1964

By D. C. Jillson

WORK in recent years1-' has indicated a complexity of the processes of deformation of metal crystals not previously appreciated and not fully accounted for by any hypothesis so far advanced. Furthermore, the nature and mechanism of formation of nuclei of recrystallization have not been determined precisely. The deformation of single crystals of zinc has been studied frequently, but the purity of the zinc and the perfection of the specimens sometimes have been given little consideration. Methods have been developed recently that readily yield zinc single-crystal specimens of high quality.5 In the present work, such specimens were deformed in various ways under various conditions, and deformed specimens were annealed to obtain information regarding recovery, recrystallization, and grain growth. The paper attempts to correlate and evaluate previous data, as well as to present new data, in order to determine areas in which more detailed work might be done most profitably. Tests at temperatures from the freezing point (419.46°C) to room temperature revealed glide only on basal planes in a close-packed direction (100)*, as reported by Mark, Polanyi, and Schmid6 and others. Markings probably similar to those observed by Kolesnikov7 and Boas and Schmid8 were noted in specimens stretched at elevated temperatures, but it seemed clear that these were not caused by prismatic or pyramidal slip (see second paragraph of section on Phenomena Involving Bending of the Basal Plane). Twinning Twinning on the octahedral plane of a face-centered cubic metal has been pictured as a process of simple homogeneous shearing along that plane in a [112] direction. It was recognized by Mathewson and Phillipsv and others""" that the (102) twinning of zinc required a somewhat more complex mechanism and might be considered as a homogeneous shearing of (102) planes in a [211] direction plus slight adjustments of atoms to positions of greater stability or lower energy, or as a single movement of each of the atoms in the same sense into the final positions. Gough and Cox" modified Mathewson's mechanism to obtain a more stable lattice configuration, but it is not clear that they succeeded, and their mechanism requires movement of some of the atoms in a sense opposite to that of the overall twinning movement. They also suggested that twinning may occur as a result of previous basal slip. This conclusion was based on the observation that twinning caused by alternating torsion was clearest and most profuse at positions for maximum basal slip rather than for maximum stress on (102) planes in the close-packed direction (not the twinning direction), and no mechanism was described. It might be wondered whether resolution of stresses on the twinning plane in the twinning direction would have afforded a simpler explanation. If twinning is essentially a simple homogeneous shearing along the twinning plane, it would seem that twins should grow by a smooth, continuous mechanism, and, indeed, that a simple reversal of stresses should reverse the shearing and de-twin the crystal. Cylindrical tablets 1/8 to 1/4 in. thick were cleaved from singlle-crystal specimens and were squeezed, perpendicular to a second-order prism plane, to give a tensile stress perpendicular to a first-order prism plane. A "click" was heard and a thin, needle-like twin appeared on the basal cleavage face. If squeezing was continued smoothly, the twin, viewed at magnifications up to X500, grew smoothly and quietly (fig. 1). X-ray examination verified that the twinning was of the (102) type. Rotating the compression axis 90" to reverse the stress then caused a smooth, continuous shrinkage and ultimate disappearance of the twin (fig. 2). The squeezing also caused a rumpling of the basal

Jan 1, 1951

By O. D. Sherby, J. E. Dorn

For elevated temperature-constant load creep tests of a solid solution alloys, the creep strain is a function of a temperature-compensated time parameter 0 = je H/RT dt. The activation energy H is equal to o constant of about 36,000 cal per mol. The substructures resulting from a given creep stress condition are functions of the creep strain independent of temperature. Each new creep stress gives a new unique set of grain substructures; this is one of the factors responsible for the failure of the mechanical equation of state for creep. IN this report an attempt is made to correlate the creep properties of dilute a: solid solutions in aluminum with the subgrain structures that are developed during creep. The possibilities of such correlations have already been suggested by Wood et al. and others1-" who demonstrated that the subgrain structures are functions of the creep stress, creep strain, rate of creep, and temperature. Investigations by Sherby and Dorn' have shown that the creep strain, E, at constant load for dilute a solid solutions of aluminum is given by the functional relationship: e = f(8,u,) [1] where: 0 equals te-AH/RT = temperature-compensated time; t, time; AH, activation energy, - 35,800 cal per mol; R, gas constant; T, absolute temperature, above 400°K; and u,, initial creep stress. Consequently, it was anticipated that the subgrain structure that develops during a constant load creep test should also correlate with any two of the three significant variables C, 8, and Another possible correlation between the subgrain structure and the creep variables is obtained by differentiating Eq. 1 with respect to time, whence the creep rate, 2, becomes: = (2L) (2) =f (, u,) e-AHRT [2] or: e = F (c e H/RT, 0) [3] For the minimum creep rate, ;,, 8 is solely a function of U, as revealed by Eq. 1. Consequently, at the minimum creep rate Eq. 3 reduces to: = F (eAH/RT) [41 Correlations between U, and i, eAH/RT were found valid for solid solution alloys of aluminum where AH was a constant of about 35,800 cal per mol. The parameter ;, eH/RT is identical to the Zener-Hollo-mon parameter8," used by them in evaluating the tensile properties of copper and other metals. Eq. 4 suggests that the subgrain structure developed during secondary creep might be correlatable with either of the two variables 2, e H/RT or u,. Some of the solid solution aluminum alloys which were discussed in an earlier report' were also used in the present investigation. Sheets of these alloys were homogenized, cold rolled from 0.100 to 0.070 in. in thickness and then recrystallized to about the same grain size. Their chemical composition and grain size are recorded in Table I. Creep specimens were selected with their tensile axes in the rolling direction. The details for creep testing have been described10 and will not be repeated here. All creep tests were performed under constant load conditions. Experimental Results and Discussion Metallographic Structure of Creep Specimens: In order to obtain a preliminary concept of creep on the metallographic structure of high purity aluminum, the various ruptured specimens previously used to obtain the creep data for pure aluminum were polished and etched electrolytically in a dilute solution of fluoroboric acid. Oblique illumination was used to reveal the substructures which, for convenience, are shown in correlation with the vs. ;, eH/RT curve in Fig. 1. It is necessary to emphasize that the data for the curve refer to the various secondary stages of creep whereas the micrographs refer to the fractured creep specimens. Nevertheless a regular and systematic correlation is observed between E, eAH/RT (or the creep stress) and the micro-structure at fracture. For In (e, eAH/RT) = 42.3, which refers to creep at a high creep rate and a low creep temperature, the fractured aluminum specimen, as shown by the micrograph in the upper right-hand corner of Fig. 1, exhibited extensive deforma-

Jan 1, 1954

By D. S. Rowley, F. C. Appl

Assuming that rock behavior, during cutting with a single diamond, may be approximated by that of a rigid, Coulomb, plastic material, a theory of single diamond cutting action has been developed. Using this theory, the stresses on the diamond cutting surface and the components of the cutting force have been determined. Theoretical results agree reasonably well with available experimental data. The theory of cutting of single diamonds may be used as the basis for subsequent study of the perfonnance of surface set diamond drill bits and other surface set diamond cutting tools. INTRODUCTION For more than twenty years, surface set diamond bits have been used successfully in the mining and petroleum industries to drill and core rock formations that range from medium hard to the hardest known formations. Most extremely hard rock formations cannot be economically drilled or cored by any other means. In view of the growing use and importance of surface set diamond drill bits, it is reasonable to study the way in which these tools cut, and the factors that influence wear of the diamonds. Such knowledge will contribute to better bit design and will improve operating procedures. To analyze the cutting performance of these tools it is appropriate to consider the way in which an individual diamond cuts. Once this is established, the over-all performance of the bits can be determined by considering the total effect of the individual diamonds. In recent years there has been a growing interest in rock mechanics and there now exist several publications dealing with the deformation and failure of rocks. Notable experimental work has been reported by Bredthauer,1 Handin and Hager,2, 3 and Gnirk and Cheatham.4 An extensive collection of data pertaining to rock properties at low confining pressures has been given by Wuerker.5 Cheatham and Gnirk have recently presented an excellent review of the state of knowledge regarding analytical and experimental rock deformation and failure.6 Generally rocks are extremely weak in uniaxial tension, and weak or only moderately strong in uniaxial compression. Both tensile failure and compressive failure are generally brittle in nature. This means that there is little or no deformation or "flow" of the material before shear or tensile fracture occurs. Thus, until fracture occurs, rock behaves very nearly like an elastic material in uniaxial stress. Significant changes in behavior of rock occur under conditions of triaxial compressive stress. There is generally a marked increase in compressive strength and in ductility. It has been demonstrated that the failure becomes plastic (in a macroscopic sense) at sufficiently high values of confining pressure. Sharp wedge chisel indentation studies conducted by Gnirk and Cheatham indicate that many rocks behave in a plastic manner at relatively low triaxial compressive stress states.4 If "failure" under triaxial compressive conditions is considered to be either complete rupture or macroscopic plastic flow, then the general failure characteristics of a rock can be reasonably well represented by the commonly known Mohr envelope. This certainly is not a perfect failure criterion (since the effect of the intermediate principal stress is neglected) but it has been found to be adequate for most engineering purposes. Mohr envelopes usually are constructed graphically using experimental triaxial test data. For purposes of analysis it is convenient to represent the envelope in equation form. Among the several approximate forms appearing in the literature, a parabolic form is suggested by Cheatham,7 and an exponential form is suggested by Paone and Tandanand.8 The exponential form has been adopted for this study, and based on published data, appropriate parameters have been established for 19 rock types. A typical plot of the data compared with the approximate envelope, and a summary of the rock properties and

Jan 1, 1969

By A. K. Mukherjee, John E. Dorn

The effects of strain rate and temperature on the critical resolved shear stress for (321)[111] slip were determined for the silver-rich CsCl type of intermetallic compound AgMg. The flow stress increased only slightly as the test temperature was first decreased below room temperature; a rapid increase in the flow stress was obtained with yet further decrease in temperature from about 250' to 4OK. The effect of both the temperature and strain rate on the flow stress over the low-temperature range could be rationalized satisfactorily in terms of the Peiwls mechanism when the deformation was controlled by rate of nucleation of pairs of kinks. IN spite of the well-documented interest of metallurgists and engineers concerning the mechanical behavior of intermediate phases and intermetallic compounds, very little definitive information is available on this important subject. As recently summarized by westbrook,1 only limited and modest progress has been made thus far in elucidating the details of the mechanism of plastic deformation for the intermetallic compounds; the available information largely concerns phenom-enological descriptions of empirical observations and experimental facts, principally with reference to poly crystalline aggregates. The present report on the elucidation of the rate-controlling mechanism for slip in the bcc structure of AgMg is part of the comprehensive program of a systematic investigation on the mechanical behavior of intermetallic compounds. The intermetallic compound AgMg has a CsCl type of lattice structureZ and is completely ordered up to its melting point of 820c3 This material was selected for our present investigation because of its simple crystal structure, moderate and congruent melting point, ordered structure persisting up to the melting point, and some solubilities of the constituent elements, which could be expected to help in the growing of single-crystal specimens. Whereas previous investigations on the properties of AgMg include hardness,*"6 slip systems,7 tensile flow stress of polycrystalline specimens,' and electrical resistivity,4 the current investigation will be directed principally at elucidating the rate-controlling dislocation mechanism responsible for slip in single crystals at low temperatures. It will be shown that the strain rate is consistent with a model involving the rate of nucleation of pairs of kinks by the Peierls mechanism for plastic deformation. EXPERIMENTAL TECHNIQUES Single-crystal specimens of the AgMg intermetallic compound were prepared and tested as follows: 1) A master alloy ingot of AgMg was produced by melting and chill casting the high-purity silver (99.995 wt pct) and high-purity magnesium (99.997 wt pct) in an induction furnace under a helium atmosphere. 2) Sections of the above-mentioned ingot were placed in a graphite mold containing a spherical cavity in which a single-crystal sphere of 1 in. diam was grown under helium by the Bridgman technique. 3) The operative slip systems were investigated at room temperature on a singlecrystal of AgMg, from measurements of the angles made by the slip traces on the two surfaces of the specimen, which were at 90 deg to each other. The investigation confirmed that the AgMg compound undergoes slip primarily in the (321) plane and in the [Ill] direction, but a small amount of secondary slip was also noticed in the (112) (111) system. No slip was observed in the (110) planes. 4) The single-crystal sphere, mentioned earlier, was oriented in a graphite mold containing a cylindrical cavity of 3/8 in. diam above the spherical receptable to give the angle xo = 45 deg between the axis of the cylindrical bar and the normal to the slip plane (321), and the angle AO = 45 deg between the slip direction [Ill] and the axis of the bar. Oriented single-crystal bar seeds were produced by melting, under a helium atmosphere, a polycrystalline bar in the cylindrical cavity above the oriented spherical seed and by growing an oriented single-crystal bar from the seed. 5) Finally, oriented single-crystal specimens were grown from these cylindrical seeds. 6) The cylindrical specimens were machined in a High-Tension Spark Cutting unit to give a 2-in. gage length. The spark-machined gage section was elec-tropolished in a bath containing 200 ml of H3PO4,

Jan 1, 1964

By Robert E. Green, P. W. Kingman

Application of a constant geometry compression test to single crystals of aluminum of selected diameters from 1/4 to 1/64 in. showed the presence of a diameter-dependmt size effect. The most pronounced effects were found in those crystals oriented for single slip, while for specimens possessing orientations in the comers of the standard stereographic triangle virtually no size effect was exhibited. The yield stress of the crystals oriented for single slip was found to increase with decrease in specimen diameter, while the strain-hardening rate was found to be lower for the smaller specimens. The experimental results are in general agreement with those of other investigators obtained from lensile tests on copper and aluminum crystals. THE earliest systematic investigation of a possible size effect on the plasticity of metals was that of no,' who in 1926 performed tensile tests on cylindrical aluminum single crystals with diameters of 3 to 8 mm. Ono concluded that the gross stress-strain curve did not show a diameter dependence, but that the resistance to slip for strains of 0.1 pet and less appeared higher for 3-mm-diam crystals than for larger sizes. Later studies of aluminum by Maddin et al2 tentatively concluded that a size effect exists, but the conclusions were again open to question because of inconsistencies in the experimental data. Wu and Smoluchowski3 had previously shown that the slip system activated in a single-crystal sheet specimen of aluminum is a function of the specimen cross section in the slip direction, but no stress-strain data were obtained. Subsequently Fleischer and Chalmers4 studied the effect of the length of the slip direction of the primary-slip system on the stress-strain curve by testing aluminum crystals with geometrically dissimilar cross sections. In the course of this investigation a size effect was indicated in rather large crystals; however, the number of these tests was small. Other investigators have indicated that a size effect in aluminum is appreciable only for diameters of 0.5 mm or less.5, 6 Size-effect studies have also been carried out on copper crystals, the most detailed being that of Suzuki et a1.7 who performed tensile tests on specimens of many diameters ranging from 2 to 0.12 mm. Suzuki found a strong size dependence in the easy-glide region, both the extent of the easy glide and the hardening rate in easy glide were size-dependent, and the size effect was found to be orientation-dependent. Suzuki's results are in agreement with the less extensive observations of Pater-sonB and those of Garstone et al.9 A size effect was found by Rebstock using tubular copper crystals.'0 Size effects have also been noted in a brass,6, 11 in cadmium,12'19 and in hexagonal crystals.14 All the previously cited works have been entirely concerned with the variation of specimen cross section. The effects of specimen length and the change of specimen geometry which results from using progressively thinner specimens while maintaining the same specimen length have been largely ignored. A theoretical discussion of the effects of specimen length and geometry has been given by Hauser and Jackson,15 who predict a grip effect on easy glide as a function of specimen geometry provided that the specimen dimensions are large compared with the spacing between the slip bands, and by Fleischer and Chalmers,18 whose analysis of grip effects resulting from lattice rotation predicts an increase in easy glide with an increase in specimen length. A study of size and geometry effects in aluminum crystals by Kitajima and shimba17 indicated increasing amounts of easy glide in specimens of increasing length and identical cross section, and nearly identical stress-strain curves for specimens of different sizes having constant length-to-diameter ratios. Since the present study is primarily concerned with diameter dependence, the following factors were taken into account: specimen material, specimen geometry, testing method, range of sizes to be tested, and possible influence of surface and volume effects. Aluminum was chosen because of the present lack of conclusive results and the seeming possibility of size effects at relatively large diameters, the

Jan 1, 1964

By H. T. Green, R. M. Brick

True stress-strain data on alloys of pure iron with up to 2.4 pct Al were obtained in the temperature range +100° to —185°C. Alumi-num was found to reduce yield and flow stresses of iron at low temperatures but to have little or no effect on ductility. The effects of temperature and composition on strain hardening are discussed. SEVERAL independent studies of the behavior of high purity iron binary alloys at low temperatures are now in progress in attempts to evaluate systematically the variables affecting the low temperature brittleness of ferritic steels. This paper reports the results of one such investigation in which the tensile properties of aluminum and aluminum plus silicon ferrites were measured from 100" to —192°C. True stress-natural strain data have been obtained in order to evaluate as many as possible of the parameters which describe the behavior of the materials involved. In comparable studies at the National Physical Laboratory in England, iron and iron alloys of high purity have been produced' and tested at subat-mospheric temperatures.' True stress-natural strain curves were obtained there also. The purest iron contained 0.0025 pct C and 0.001 pct O and N. Even this, as normalized at 950°C following hot rolling, showed little ductility at -196°C. The grain size was ASTM No. 3, and the room-temperature yield strength was 17,800 psi (which seems too high for pure iron). Some of the NPL irons contained considerably more oxygen and demonstrated intergran-ular fracture at —196°C. The authors2 carefully differentiated between intergranular fractures associated with excessive oxygen content and transcrys-talline cleavage with little ductility encountered at —196°C in the purer material. The cleavage stress was half again as great as that associated with inter-granular fracture. Test Material, Preparation, and Procedures Of a number of Fe-A1 alloys produced, eight were considered to be sufficiently pure for testing. Partial chemical analyses (Table I), low observed yield points, and high ductilities indicate these alloys to be comparatively pure for vacuum-melted irons of sizable ingots, 5 Ib or more. To produce the binary Fe-A1 alloys, electrolytic iron was melted in air, cast into slabs, and rolled to strips 0.010 in. thick. These strips, joined into a continuous ribbon and wound into 2 1/2 in. diameter spools, were subjected for four weeks to a moving atmosphere of purified dry hydrogen in a stainless-steel tube at 1050" to 1150°C. Charges of these spools were melted in beryllia crucibles under good vacuums (1 micron), and aluminum (99.97 pct Al) was added to the melts. Compositions of these alloys are recorded in Table I. The ingots were hot forged and then cold rolled at least 65 pct to 3/8 in. rods which were vacuum annealed to the desired grain size, approximately ASTM No. 4, prior to machining into tensile test bars. All tensile specimens had gage sections 1 in. long, with a fillet of 1.5 in. radius to the shoulder. Gage diameters were 0.250 in, except for a few rods where additional cold work required use of a 0.200 in. gage section. After machining, 0.002 in. was removed from the gage diameter using 240, 400, and 600-grit metallo-graphic papers. The final polish with 600 grit left the fine scratches running in the longitudinal direction. By this means, surface metal strained during machining was removed. A few specimens heat treated after machining were similarly reduced 0.004 in. to remove any material affected chemically by the atmosphere during heat treatments, as is discussed in a later section. Tensile tests of the eight alloys at constant temperatures from +100° to —185°C were performed in apparatus which has been described." The essentials include a double-walled insulated metal vessel which contained the liquid heat-transfer medium surrounding the test specimen. A constant temperature was maintained by means of a pyrometer which regulated the pressure of dry air driving liquid air through a copper coil. Temperature variation was less than ±2°C during a specific test. For axial straining, two lengths of case-hardened chain, terminating in simple shackles, loaded the specimen through threaded grips. The lower grip bar passed through a hole in the bottom of the test vessel to which it was joined by a thin-walled

Jan 1, 1955

By Colin Baker, G. C. Smith

Investigation of the initiation and propagation of ductile failure in OFHC copper was undertaken to determine the role of nonmetallic inclusions. The effect of inclusion initiated voids on the formation of the internal cavity and the final shear separation was studied by metallographic eranzination of strained test pieces. A strain anneal technique was used to enlarge the voids under uniaxial stress conditions to elinzinate triaxial stress effects. Measurements of void size us stress and strain were made to show the point at which void im'tiation begins and becomes an important factor in the deformation process. The work of separation of copper-cuprous oxide was determined to attempt to correlate the breakdown of the matrix inclusion interface with void initiation and propagation. The zloid shape and position relative to the tensile axis suggested an interface breakdown mechanisnz of initiation. Evidence is presented that shows a basic similarity between the central cavity propagation and the 45-deg shear portions of the failure. DUCTILE fracture has been studied by a number of workers1-lo and attention drawn to the importance of hard second phase particles in the initiation of the failure. Holes formed at the matrix-particle interface can elongate by plastic deformation and then subsequently expand sideways to link up and produce a major crack. This is usually observed first in the center of the macroscopically necked region of a test-piece where the hydrostatic stresses are at a maximum. As the crack spreads sideways towards the free surface of the specimen, well defined shear zones develop from the crack tip and the final separation is along a direction at approximately 45 deg to the stress axis. This shear failure may also be associated with voids formed adjacent to second phase particles. In this way a cup and cone type fracture is produced. The stage at which separation takes place between particles and the surrounding matrix has not been clearly identified. In addition, although researchers have dealt with anisotropy of tensile behavior" as a result of material fabrication variables, not much is known about the microstructural features of aniso-tropic behavior. In the present work evidence on these points is presented in relation to the behavior of copper containing second phase particles of cuprous oxide. I. MATERIALS AND PROCEDURES EMPLOYED The material used was +-in. diam or 2-in. sq cold-drawn OFHC copper bar which contained 0.6 pct by volume of cuprous oxide inclusions. These ranged in COLIN BAKER, Junior Member AIME, formerly at -mnF of Metallurgy, University of Cambridge, Cambridge, England, is presently Research Scientist Reynolds Metals Co., Richrnand, Va. G. C. SMITH, Member AIME, is Senior Lecturer, Department of Metallurgy, University of Cambridge. Manuscript submitted June 20, 1967. IMD size from approximately 1 to 6 p in length and 1 to 4 p in width. The shape was generally slightly ovoid. Tensile tests were made on specimens having a gage length of 2.5 cm and diameter of 0.643 cm. Metallographic examination was carried out by sectioning deformed and fractured specimens; in addition fracture surfaces were examined optically and with a scanning electron microscope. Some measurements of the work of separation between copper and cuprous oxide were made, using a sessile drop technique which was a modification of that used by Kingery and umenick." The best metallographic results were obtained by using a vibratory polisher, which minimized smearing of the surface. 11. RESULTS A) Initial Experiments. Specimens from the +-in. diam rod were annealed for 2 hr at 650°C in uacuo, at which temperature complete recrystallization occurred without any change in the form of the inclusion. They were then fractured at temperatures from -190" to 600°C. Cup and cone fractures were obtained at all temperatures from -196" to 400°C. With increase in temperature there was, however, a continuous increase in the extent of the central transverse area and a corresponding decrease in the shear portion of the fracture. Above 400°C, the fractures became intergranular. Sections of specimens tested below 400°C revealed extensive small voids which were always associated with inclusions. However, the voids only reached dimensions greater than the inclusion size in the region of the macroscopic neck, where they were many times longer. Lateral expansion was found only near the fracture surface of the test pieces. As observed by Puttick, the voids were either (a) triangular holes initiated in the direction of the tensile axis and elon-

Jan 1, 1969

By H. E. Mauck

The many factors that control bumping must be carefully studied for each coal seam where bumps occur, and specifications known to exclude bumping should be incorporated in the mining plans. This calls for complete knowledge of the seam's characteristics and its adjacent strata, and in many instances these characteristics are not revealed until the seam is actually mined. Pressure and shock bumps, the two general types, occur jointly and separately. In this discussion no differentiation will be made. Whether pressure or shock, they are treated as bumps, and both must be eliminated. Bumps in mines have occurred in several places throughout the coal fields of the world. A study of many of these occurrences indicates that geologic characteristics, development planning, and mining procedure have contributed. But more specifically, there are conditions usually associated with bumps: thickness of cover, strong strata directly on or above the seam, a tough floor or bottom not subject to heaving, mountainous terrain, stressed and steeply pitching beds, and the proximity of faults and other geologic structures. Mine planning should incorporate these known factors (not necessarily in order of importance): 1) Main panel entries should be limited to those absolutely necessary to ventilate and serve the mine. This reduces the span over which stresses may be set up that will later throw excessive pressures on barrier and chain pillars when they are being removed. 2) Barrier pillars should be as wide as practicable so that they will be strong enough to carry the loads thrown on them when final mining is being carried out. 3) Pillars should never be fully recovered on both sides of a main entry development if the barrier and chain pillars are to be removed later. The excessive pressures placed on the main chain and pillar barriers by arching of the gob areas can result in bumping when these barriers are being removed. 4) Full seam extraction is better accomplished by driving to the mine boundary and then retreat-drawing all pillars. If there are natural boundaries in the mine—such as faults, want areas, and valleys —retreat should be started there. 5) Pillars should be uniform in size and shape. The entire development of the mine should call for uniform blocks with entries driven parallel and perpendicular. Only angle break-throughs should be driven when necessary for haulage, etc. 6) For better distribution of rock stresses and reduction of carrying loads per unit area, both chain and barrier pillars should be developed with the maximum dimensions. 7) Pillars should be open-ended when recovered. If they are oblong, the short side should be mined first. Both sides of a block should not be mined simultaneously, but under no circumstance should the lifts be cut together. 8) Pillar sprags should not be left in mining. If they are not recoverable, they should be rendered incapable of carrying loads. 9) Pillar lines should be as short as practicable. (Three or four blocks are adequate). Experience has shown that rooms should be driven up and retreated immediately. The longer a room stands, the more unfavorable the mining conditions. This contributes to bumping. 10) Pillars should not be split in abutment zones (high stress areas lying close to mined out areas) and if slabbing is necessary, it should be open-ended. 11) Pillars should be recovered in a straight line. Irregular pillar lines will allow excessive pressures thrown on the jutting points. Experience has shown that the lead end of the pillar line can be slightly in advance. 12) Pillar lines should be extracted as rapidly as possible. This appears to lessen pressures on the line and render abutment zones less hazardous. 13) Extraction planning should call for large, continuous robbed out areas. Robbing out an area too narrow to get a major fall of the strata above the seam tends to throw excessive pressures on a pillar line. 14) Timbering in pillar areas should be adequate but not excessive. Too heavy timbering or cribbing is likely to retard roof falls and throw excessive weight on the pillar line. 15) Experience has shown that when pillar lines have retreated 800 to 1000 ft from the solid, bumps can occur. Because this distance may vary in different seams, impact stresses should be studied for each individual condition. In any event, extra precautions should be taken against bumps in this area. This list of controlling factors may or may not be complete. It probably is not, but it covers most of the problem's significant aspects. The question is whether or not bumping can be eliminated. The answer is that bumping can be minimized and possibly eliminated if these and other established factors are thoughtfully considered and incorporated in the mining and extraction plans. If a mine has already been developed or the pattern set so that little change can be made, then it will be necessary to adjust to the most nearly practicable system that can incorporate the known factors.

Jan 1, 1959

By J. W. Edington

THE Hopkinson bar has become a popular technique for the measurement of the mechanical properties of materials deformed at high strain rate. Maximum use of the equipment is made in the arrangement first used by Kolskyl in which a short compression specimen is sandwiched between two pressure bars and is loaded by a single pulse travelling through the system. The pressure bars are used both to apply the load to the specimen and as transducers to obtain continuous strain-time histories of three pulses, incident on, reflected, and transmitted by the specimen. The data measured by the pressure bars can be analyzed in terms of the stress/strain behavior of the specimen.2'3 However, one of the assumptions of the analysis of the observed pulses is that the total stress and total strain do not vary significantly from point to point within the specimen at any given instant during the deformation process. Although this assumption is generally justified for very short disc-like specimens2 the situation is uncertain for larger specimens. For example, at small plastic strains (-0.01) Hauser et al.2 have some evidence of small flucations in the total stress within the crystal during deformation, even in relatively short aluminum specimens. In addition, Karnes4 has shown that the plastic strain, and by inference strain rate, is different at each end of a compression specimen tested in a Hopkinson bar, although the length of the specimen was not specified. Recently, the mechanical properties and the dislocation substructure have been investigated in single crystals of columbium5 (length 0.25 in., diam 0.19 in.), and copper6 (length 0.5 in., diam 0.5 in.) deformed at high strain rates. As part of this research program the assumption that the plastic strain is constant throughout the specimen has been checked by measuring the total dislocation density as a function of position in the specimen. Compression specimens of the same orientations and dimensions were tested as described previously5,6 sing a split Hopkinson bar. Since any discontinuity in strain distribution is most likely to arise during the initial stages of deformation the investigation was performed on specimens deformed to plastic shear strains of 0.054 (copper) at a strain rate 1.2 x l03 sec-1, and 0.06 (columbium) at a strain rate 1.5 X l03 sec-1. The orientation of the single crystals is shown in Figs. 1 and 3. Thin foils were taken parallel to the most highly stressed slip plane, i.e., (111) in copper and (011) in columbium, using conventional disc techniques. The dislocation densities were measured using first order reflections with compensation for invisible dislocations.5'6 In the copper single crystals the discs were randomly distributed throughout the cross section of the specimen. However, the dislocation density obtained from each disc was plotted vs the disc positions relative to the ends of the specimen. The results for the copper specimens are shown in Fig. 1. Clearly the dislocation density is constant throughout the main portion of specimen within the experimental error. The error bars on the dislocation densities correspond to a shear strain variation of 0.015 on the basis of previous measurements% ± of the rate of increase of dislocation density with strain in copper single crystals of the same geometry. Thus within this experimental error the plastic strain can be concluded to be constant within the specimen and the assumptions used in the analysis of the stress/time curves are therefore reasonably valid. The higher measured dslocation density near the impact end and the lower dislocation density at the bar end of the copper specimen is in agreement with the results of Karnes4 who showed that this strain/time curve rose to a maximum more rapidly at the impact end compared with the bar end. Hauser et al.2 have also pointed out that at small plastic strains (-0.01) the strain at the impact end of the specimen may be greater than that at the bar end. Thin foils taken from different points within the columbium single crystals demonstrated that the dislocation density could vary significantly within the specimen, see Fig. 2. Large areas of some thin foils up to 30 µ sq contained very few dislocations, see Fig. 2(a). However, in other parts of the compression specimen dislocation configurations like those shown in Fig. 2(b) existed over large areas (-30 µ sq). As a result, when the average dislocation density in a thin foil is plotted as a function of the position of the thin foil relative to the ends of the specimen, considerable scatter is observed, see Fig. 3. In this material then, the local dislocation density, and consequently the

Jan 1, 1970

By G. R. Leverant, C. P. Sullivan

To evaluate the effect of a dispersion of nondeform-able, incoherent, second-phase particles on high-strain cyclic deformation and fracture, recrystallized TD-nickel (Ni-2ThO2) and a commercially pure nickel, Ni-200, were fatigued under strain control at total strain ranges varying from 0.009 to 0.036. Relative to the Ni-200, the slip at the surface of the TD-nickel was more wavy and discontinuous due to the presence of the thoria particles. This made crevice formation (incipient cracking) within slip bands more difficult in TD-nickel than in Ni-200. Both materials cyclically hardened to a constant (saturation) flow stress which increased with increasing plastic strain amplitude. Cellular substructures were developed in both materials during cycling. The cell size in TD-nickel was controlled by the thoria particle distribution and was independent of plastic strain amplitude over the range investigated. The cell size in Ni-ZOO was larger than that in TD-nickel at similar plastic strain amplitudes and was a function of plastic strain amplitude. These results, together with the cyclic stress-strain curves for both materials, are discussed in terms of a model for fatigue strain accommodation at saturation recently proposed by Feltner and Laird. NUMEROUS fatigue investigations have considered the interrelation of slip character, dislocation substructure, and cracking in pure metals and solid-solution alloys. However, except for the studies of the low-strain fatigue of internally oxidized copper alloys1 and cast, dispersion-strengthened lead,&apos; little is known about the effects which small, incoherent, nondeform-able, second-phase particles have on cyclic deformation and cracking processes. Effects due to the particles alone are often obscured by a dislocation substructure introduced during thermomechanical processing of dispersion-strengthened metals. In the present study, recrystallized TD-nickel and a commercially pure nickel, Ni-200, were employed to evaluate the effect of a thoria dispersion on high-strai fatigue deformation and cracking at room temperature. I) MATERIAL AND EXPERIMENTAL PROCEDURE The TD-nickel was supplied by DuPont as a 5/8-in.-thick stress-relieved plate which had been subjected to a proprietary schedule of thermomechanical treatments, and the Ni-200 as 3/4-in. bar which was subsequently annealed for 2 hr at 850°C in argon resulting in an average grain diameter of 0.05 mm. The compositions of these materials are given in Table I. The microstructure of the TD-nickel consisted of elongated grains parallel to the primary working direction with an average width of 0.16 mm, Fig. l(a). Many fine annealing twins were present indicating that the starting material was in a recrystallized condition; this supposition was confirmed by the absence of of any extensive dislocation substructure, Fig. l(b). Sheetlike stringers parallel to the rolling direction were occasionally seen both within grains and at grain boundaries. Some approximately spherical particles about 2 in diam, which may correspond to exceptionally large thoria particle aggregates, were also present. The average Young&apos;s modulus of the plate material in the rolling direction was 21.8 X 106 psi which is consistent with a {100}<001>recrystalliza-tion texture3&apos;* being prominent. In transmission microscopy, the 2.3 vol pct of thoria particles generally appeared to be uniformly distributed although some clusters, 0.1 to 0.3 in diam, of larger particles were observed as previously reported for TD-nickel sheet,5 and stringering of particles was present in some areas as welt. The average diameter of the thoria particles was 450A with a calculated mean planar center-to-center spacing of 2100A, as determined by quantitative metallographic analysis.= The 0.2 pct offset yield stress was 36,000 psi which agrees with the value predicted by the modified Orowan relation7 for edge dislocations bowing between thoria particles of the size and spacing observed in the present investigation. Fig. 2 illustrates the specimen design employed for the axial high-strain fatigue testing. Adapters were screwed onto the threaded portions of each specimen so that testing could be performed in the same manner as that reported for buttonhead specimens.8 Stressing was coincident with the working direction for both materials. The gage section of each specimen was electropolished and lightly etched prior to testing. The total strain was controlled, being varied between zero and a maximum tensile strain ranging from 0.009 to 0.036. In addition to these tests, a circum-ferentially notched TD-nickel specimen was cycled over a total strain range of 0.0075. The same strain

Jan 1, 1969

By D. L. Creighton, S. A. Hoenig

The field-emission microscope has been adapted for the study of microcrack growth during the early stages of fracture in metal wires. Cracks as small as 6 1 in length can be detected and their growth can be followed to specimen failure. The system is quite useful in searching for microcracks since only sharp-edged surface defects will emit electrons under the experimental conditions. THE conditions leading to brittle fracture were discussed a number of years ago by Griffith1 and the term Griffith Cracks is often used for the small surface cracks which are responsible for brittle fracture. Griffith&apos;s theory has been modified by stroh2 and more recent results on metals are discussed by Allen,3 pp. 123-40. At present the phenomenon is not completely understood but there is general agreement that at least in certain materials the sequence leading to brittle fracture involves several stages. The initial microcracks are present because of cooling or working stresses, Hahn et al.,3 p. 95. When a stress is applied to the specimen the cracks grow slowly until the release of stored elastic energy is large enough to accelerate the crack and provide the necessary surface energy for crack growth. At this point the growth rate appears to increase rapidly to some new equilibrium velocity, and failure occurs. Since the microcracks are usually about the size of a single metallic grain (Ref. 3, p. 99) it is not easy to find them and it is very difficult to follow their growth under stress. This paper will report on the use of a cylindrical field-emission microscope for observation of the formation and growth of microcracks. I) THE FIELD-EMISSION MICROSCOPE The field-emission microscope (FEM) has a high magnification and resolution and is almost uniquely suited for observations of microcracks. Since the FEM is relatively new as a metallurgical instrument, a short description will be given here. Normally metals at room temperature do not emit electrons; however in the presence of a strong electric-field gradient, electrons can tunnel out through the reduced potential barrier. Since this tunneling is a function of the local field gradient and the local work function, the emitted electrons can be used to produce a highly magnified image of the surface by allowing them to strike a phosphor screen. Because the electron emission is dependent upon the local field gradient, smooth surfaces emit few electrons except at very high fields. On the other hand cracks, extrusions, or other surface defects, having sharp edges, emit strongly since the field gradient is very high in the vicinity of these defects. This indicates that the FEM should be most useful for detection of microcracks on otherwise smooth surfaces. A field-emission microscope was first used by Muller4 in 1936 for observation of metal surfaces, and recent reviews have been given by Muller5 and Gomer.6 The instrument has been used for metallurgical studies in the area of surface diffusion,= recrystallization,7 and grain growth 8 (Ref. 8 is directed specifically at metallurgists). In the work of Muller4,5 and Gomer 6 the specimen was in the form of a sharp metal point at the center of a phosphor-coated glais sphere. The impact of the emitted electrons on the phosphor produced a highly magnified image of the specimens. Such a system is not practical for applying a controlled stress to the specimen and a cylindrical geometry has been used in this investigation. This allowed the application of a controlled tensile stress to the wire specimen. Normally a cylindrical FEM geometry produces magnification only in the radial direction. This is the case because a smooth wire at the center of a cylinder produces a purely radial electrical field. However, if there is a break in the smooth surface of the inner cylinder, the field near the break becomes three-dimensional and the area of the break is highly magnified. The reason for this is clear if it is recalled that the field gradient depends on the relative radii of the inner and outer cylinders; if a crack forms, its edge radii are of atomic dimensions and a very high field gradient is formed near these crack edges. Since the electrons receive most of their acceleration near the crack edge and are always traveling perpendicular to the field lines, they tend to spread out and produce the magnified image observed in the cylindrical field-emission microscope. 11) BRITTLE-FRACTURE STUDIES A) Experimental Apparatus. The geometrical arrangement chosen was that used earlier by Gifford

Jan 1, 1965

By R. C. Padfield

Experience over a 3-year period in Bethlehem Steel Corporation&apos;s plants has demonstrated the reliability of open-hearth roofs of bonded sprung-arch constructzon with burned basic brick. The design principles lor constructing these roofs include a minimum hot-strength requirement for the basic brick, expansion allowances that extend the full roof thickness, structural members to control arch contour, and a specified minimum roof rise. The greater stability of bonded roofs is explained in terms of the basic stress patterns of ring constrution and bonded construction. PRIOR to the development of successful sprung-arch roofs of basic brick, the majority of open-hearth furnaces in the United States were operated with sprung-arch roofs built of silica brick. Although many silica roofs used on open-hearth furnaces were ring-arch construction, Bethlehem Steel Corp. used bonded-arch construction because of its greater stability. In ring construction, each ring of brick is separately keyed and comprises an independent arch with the straight joints between rings traverse to the longitudinal axis of the furnace. In bonded construction, the bricks are laid in rows starting from the skewbacks so that the straight joints run parallel to the longitudinal axis of the furnace. Each brick in a given row is laid so that it spans the joint between two bricks in the row beneath it. Thus, the transverse joints across the arch are broken and the arch rings are thereby interlocked or bonded. When basic roofs were first being developed, the basic brick that were available had low hot strength. Such brick could not be safely used in sprung-arch construction without some means of suspending them. With the development of higher firing techniques by brick manufacturers and the recently introduced direct bonded bricks with high hot strength, the use of burned basic brick in sprung-arch roofs became feasible. The availability of high hot strength basic brick coupled with the potentially lower cost and proven stability of bonded construction prompted Bethlehem&apos;s Research Department to study the possibility of using basic brick in bonded roofs. With the full cooperation of plant ceramic engineers and open-hearth superintendents, particularly in 3 years of fur-nace trials, we developed the design criteria for bonded roofs and the corresponding property requirements for the basic brick that are discussed in this paper. DESIGN PRINCIPLES OF SPRUNG-ARCH BRICK ROOFS Stresses in Fixed Arches. A sprung-arch open-hearth furnace roof is generally built on rigidly held skewbacks. The constraint of the fixed support at each end adds a bending moment to the horizontal and vertical reactions at the ends of the arch. Fig. 11 shows the positive direction of forces acting on an arch fixed at both ends. Fixed arches can be analyzed when the members are continuous and have elastic properties. However, brick are inelastic, and arches built with individual brick segments cannot carry tensile stresses. Therefore, for practical solution of brick arches, empirical formulas have been derived from elastic theory that place design restrictions on arch dimensions to avoid development of tensile stresses. McDowell2 cites three main conditions for stability in sprung brick arches: 1) the thrust line of the arch should be maintained in the middle third of the thickness to avoid tensile stresses and resulting open joints in inner and outer curves of the arch; 2) the angle between the line of thrust at any joint and a line perpendicular to the joint must not exceed the angle of repose between brick; and 3) the maximum pressure at any point must not exceed the strength of the arch materials at furnace operating temperatures. The first and third conditions are particularly important in designing sprung-arch basic roofs because of the comparatively low hot strength of basic brick. According to McDowell&apos;s equation, if the thrust line is maintained within the middle third of the arch thickness, the unit pressure is obtained as follows: where p = unit pressure in psi, F, = resultant thrust normal to skewback in pounds per foot, t = arch thickness in inches, and z = distance in inches of thrust line from arch axis. When the resultant thrust normal to the skewback acts along the arch axis, z equals zero and unit pressure is simply the thrust divided by the cross-sectional area. If the thrust line moves to the limits of the middle third of the arch thickness, beyond which tensile forces would develop, z then equals one-sixth of the arch thickness and the unit pressure is double that when the thrust line is acting

Jan 1, 1968

By L. D. Hall, D. R. Mash

The paper presents the results of experiments on the anelastic. behavior of gold, as manifested by grain boundary relaxation. Two grain boundary internal friction peaks are found for 99.9998 pct Au. It is found that the peaks are associated with primary and secondary recrystallization. However, the existence of two discrete peaks cannot be explained on the basis of grain size and shape alone. It is suggested that grain boundary stability, as determined by orientation, plays a role in the observed effects. EVIDENCE for the viscous behavior of grain boundaries in metals has been presented in recent years by several investigators, based upon studies of various anelastic effects, especially internal friction. KG1 has contributed greatly to this field, having put forward a coherent body of evidence for stress relaxation by the viscous intercrystalline flow mechanism. In this connection, he has made extensive use of pure aluminum (99.991 pct) as the test material, although he has also studied other metals and alloys, including pure iron (Puron).² Rotherham, Smith, and Greenough³ have studied the internal friction of pure tin, interpreting their results in a manner similar to that of KG. In view of the importance of such studies in shedding light upon the fundamental structure and behavior of the grain boundaries in pure metals, it appears that the use of a very pure test material which is inert to its environment should provide useful information on anelastic properties and the source of such behavior in pure metals. The present work was carried out on spectrograph-ically pure, 99.9998 pct Au, free of all impurities except for a trace of silver, estimated to be present to the extent of about 0.0002 pct. The term "pure gold" will hereafter refer to this very pure material. Gold of commercial purity, 99.98 pct, was also studied to observe the effects of small amounts of impurities. A pure gold "single crystal" specimen was also tested for comparison. The variation of the internal friction and rigidity modulus as a function of temperature was determined by means of a torsion pendulum apparatus employing extremely low stress amplitudes and a frequency of vibration of the order of 1 cycle per sec. A 12 in. length of 0.031 in. (20 gage) gold wire formed the suspension element. The apparatus was similar to that described by Ke.l The test procedure and the basic requirements to be met for obtaining useful experimental data by this method have been given elsewhere.1,2 It should be made clear that in all of the experiments to be described, the internal friction and rigidity were independent of the amplitude of torsional vibration. The semilog plot of amplitude of vibration vs ordinal number of vibration was a straight line. This was carefully verified for each internal friction measurement. The linear variation shows that the internal friction was independent of stress; i.e., that the specimens were not being cold-worked during testing. The reproducibility of the internal friction curves, which were obtained by cyclic heating and cooling, indicates that the gold was unaffected by its environment during the tests. The measure of internal friction adopted in the present study is the conventional "logarithmic decrement," defined as follows: log. dec. = l/n In A0/An [I] where n is the number of cycles or vibrations; A,, the initial amplitude of vibration; and An, the amplitude after the nth cycle. When the logarithmic decrement is small, the shear modulus, G, of the wire is proportional to the square of the frequency of vibration provided the length and radius of the wire are kept constant. A plot of frequency squared vs temperature gives the following ratio:&apos; This expresses the fraction of the stress which has not been relaxed at a given temperature. Gr and Gv are the relaxed and unrelaxed moduli, respectively. The frequency of vibration in the polycrys-talline specimen is fp, and the frequency of vibration of a single crystal is f8. This latter quantity is obtained simply by extrapolating the linear, low temperature portion of the curve of frequency squared vs temperature for the polycrystalline specimens. The theory of viscous grain boundary stress relaxation as demonstrated by the anelastic behavior of metals has been discussed in detail by Zener4 and need not be reproduced here. Experimental Results Initial measurements of the internal friction of pure gold were carried out on specimens which had been drawn with no intermediate annealing, resulting in a material which had undergone approximately 99 pct reduction of area in final processing. Annealing was then carried out at successively higher temperatures starting at 400°F for 1 hr and proceeding in this manner to as high as 1600°F in 100°F intervals. After each annealing treatment an internal friction and rigidity vs temperature curve was obtained over the range from room temperature to the particular annealing temperature. The resulting internal friction curves did not exhibit well defined maxima (peaks), but rather several fairly flat

Jan 1, 1954