METALLURGICAL AND MATERIALS TRANSACTIONS A
ABSTRACTS
Volume 27A, No. 4, April 1996

This Month Featuring: Symposium on High Temperature Fracture Mechanisms in Advanced Materials; Alloy Phases; Transformations; Transport Phenomena; Mechanical Behavior; Physical Chemistry; Surface Treatment; Solidification and Materials Processing. View April 1996 Table of Contents.

SYMPOSIUM ON HIGH TEMPERATURE FRACTURE MECHANISMS IN ADVANCED MATERIALS

Foreword
Advances in materials processing in the last few decades and an ever-increasing demand for materials with improved high temperature properties has recently led to the rapid development of new metallic alloys, composites, and ceramics on a scale never before seen. With this development, it has become increasingly evident that a clear understanding of the failure mechanisms in many of these new materials at elevated as well as ambient temperatures must be achieved before they can be used in practical applications. Naturally, such an understanding minimizes the risk of unforeseen catastrophic failure during high temperature service. In addition to achieving this goal, however, a thorough knowledge of fracture behavior at elevated temperatures also assures that the properties and service conditions of high temperature materials are optimized in a manner which more than justifies their cost.

It is in the spirit of this growing need for information that the present symposium was organized under the sponsorship of the ASM/MSD Committee on Flow and Fracture. The symposium was held in Rosemont, Illinois as part of the 1994 Materials Week/TMS Fall Meeting. The symposium consisted of four sessions which covered high temperature crack growth under static loading conditions, crack growth under cyclic loading conditions, damage mechanisms in advanced alloys and model materials, and damage processes in recently developed composite materials. The following papers were peer reviewed under the normal process for Metallurgical and Materials Transactions and are representative of the presentations included in the symposium. We feel that these papers also represent the type and quality of research that must be accomplished for the further development and successful application of advanced high temperature materials.

We wish to thank all our colleagues and co-workers who participated in the symposium and contributed manuscripts for publication. In particular, the time and effort of the session chairs and the TMS Meetings Department staff in conducting the symposium is greatly appreciated. Finally, we wish to thank Prof. David Laughlin, Editor, and Ms. Dora Moscatello, Production Editor, Metallurgrical and Materials Transactions, for taking the following papers through the normal review process as a single proceedings.

Prof. James C. Earthman
Materials Science and Engineering
University of California
Irvine, CA

Dr. Kwai S. Chan
Southwest Research Institute
San Antonio, TX

Creep Deformation and Crack Growth Behavior of a Single-Crystal Nickel-Base Superalloy
S.J. MOSS, G.A. WEBSTER, and E. FLEURY
Uniaxial creep deformation and crack growth data are presented on the single-crystal nickel-base superalloy SC16, which is a candidate material for industrial gas turbine applications. All testing was performed at 900°C. The uniaxial experiments were conducted with the loading direction aligned approximately along the [001] crystallographic axis of the material. Under these conditions, a small primary region followed by mainly tertiary creep was obtained, and failure initiated from cracks at interdendritic pores. The crack growth experiments were performed on single-edge notch tension specimens and compact tension test pieces containing deep side grooves to examine state-of-stress effects. A selection of crystallographic orientations was also examined. Little effect of stress state and orientation was obtained. It has been found that the creep crack growth characteristics of the alloy can be predicted satisfactorily from a model of the accumulation of damage at a crack tip using the creep fracture mechanics parameter C * and assuming plane stress conditions.

Time-Dependent, Environmentally Assisted Crack Growth in Nicalon-Fiber-Reinforced SiC Composites at Elevated Temperatures
C.H. HENAGER, Jr., R.H. JONES, C.F. WINDISCH, Jr., M.M. STACKPOOLE, and R. BORDIA
Subcritical crack growth measurements were conducted on ceramic matrix composites of -SiC matrix reinforced with NICALON fibers (SiC/SiCf); fiber-matrix interphases were of carbon andboron nitride. Velocities of effective elastic cracks were determined as a function of effective applied stress intensity in pure Ar and in Ar plus 2000, 5000, and 20,000 ppm O2 atmospheres at 1100°C. Over a wide range of applied stress intensities, the V-Keff diagrams revealed a stage II pattern in which the crack velocity depends only weakly on the applied stress intensity, followed by a stage III, or power-law, pattern at higher stress intensity. Oxygen increased the crack velocity in stage II and shifted the stage II to III transition to the left. A two-dimensional (2-D) micromechanics approach, developed to model the time dependence of observed crack-bridging events, rationalized the measured effective crack velocities, their time dependence, the stage II to III transition, and the effect of oxygen in terms of the load relaxation of crack-bridging fibers.

Mechanisms of High-Temperature Fatigue Failure in Alloy 800H
K. BHANU SANKARA RAO, H. SCHUSTER, and G.R. HALFORD
The damage mechanisms influencing the axial strain-controlled low-cycle fatigue (LCF) behavior of alloy 800H at 850°C have been evaluated under conditions of equal tension/compression ramp rates (fast-fast (F-F): 4 x 10-3 s-1 and slow-slow (S-S): 4 x 10-5 s-1) and asymmetrical ramp rates (fast-slow (F-S): 4 x 10-3 s-1 / 4 x 10-5 s-1 and slow-fast (S-F): 4 x 10-5 / 4 x 10-3 s-1) in tension and compression. The fatigue life, cyclic stress response, and fracture modes were significantly influenced by the waveform shape. The fatigue lives displayed by different loading conditions were in the following order: F-F > S-S > F-S > S-F. The fracture mode was dictated by the ramp rate adopted in the tensile direction. The fast ramp rate in the tensile direction led to the occurrence of transgranular crack initiation and propagation, whereas the slow ramp rate caused intergranular initiation and propagation. The time-dependent processes and their synergistic interactions, which were at the basis of observed changes in cyclic stress response and fatigue life, were identified. Oxidation, creep damage, dynamic strain aging, massive carbide precipitation, time-dependent creep deformation, and deformation ratcheting were among the several factors influencing cyclic life. Irrespective of the loading condition, the largest effect on life was exerted by oxidation processes. Deformation ratcheting had its greatest influence on life under asymmetrical loading conditions. Creep damage accumulated the greatest amount during the slow tensile ramp under S-F conditions.

Effect of Fe on Ductility and Cavitation in the Superplastic Zn-22 Pct Al Eutectoid
XING-GANG JIANG, SUSAN T. YANG, JAMES C. EARTHMAN, and FARGHALLI A. MOHAMED
In this investigation, the ductility and cavitation behavior of five grades of the superplastic Zn-22 pct Al were studied under identical conditions of grain size, temperature, and initial strain rate. These five grades were prepared from high-purity Al and Zn using the same procedure but different Fe impurity levels; grades A, B, C, D, and E contain 1, 40, 120, 400, and 1460 ppm of Fe, respectively. A comparison between the present results and those reported earlier for the creep behavior of the five grades of Zn 22 pct Al demonstrates that while the presence of Fe has no noticeable effect on the steady-state creep rates during deformation in the superplastic region (where maximum ductility occurs), it has a pronounced effect on the ductility and fracture behavior of the alloy. The experimental data show that there is a significant drop in the average elongation to fracture when Fe concentration exceeds 125 ppm, and that the ductility of grade E is approximately 50 pct of grade A for initial strain rates less than 10-2 s-1. In addition, the data reveal two important findings regarding cavitation behavior. First, neither the initial grain size nor the occurrence of grain growth has an effect on cavitation that is as significant as that arising from the presence of excessive impurities. Second, the presence of other impurities in addition to Fe in Zn-22 pct Al has the effect of enhancing cavitation. The effect of Fe, alone or in the presence of other impurities, on ductility and cavitation in Zn 22 pct Al is examined in terms of phenomena associated with impurity segregation at boundaries.

The Characteristics of Cavitation in Superplastic Metals and Ceramics
YAN MA and TERENCE G. LANGDON
It is now well established that cavities are often formed during superplastic deformation. However, experimental investigations suggest important differences in the nature of the cavitation in typical superplastic metals and ceramics. These differences are demonstrated with reference to a superplastic Cu-based alloy and yttria-stabilized tetragonal zirconia (Y-TZP). By using a quantitative metallographic procedure and scanning video images, measurements are presented showing the size, shape, and configuration of internal cavities in these two materials after deformation at high temperatures.

On the Influence of Grain Morphology on Creep Deformation and Damage Mechanisms in Directionally Solidified and Oxide Dispersion Strengthened Superalloys
B. DeMESTRAL, G. EGGELER, and H.-J. KLAM
Directionally solidified (DS) and oxide dispersion strengthened (ODS) superalloys like CM 247 LC and MA 760 exhibit elongated macrograins. In uniaxial creep tests, the creep strength of such alloys in the direction of the longitudinal grains is higher than that of an equiaxed grain structure, because significantly less grain boundary (GB) segments are perpendicular to the axis of the applied stress. The present study investigates how creep in the longitudinal direction of these alloys is influenced (1) by deviations of individual grain orientations from the optimum growth direction during casting (CM 247 LC) and (2) by the spatial distribution of the small transverse GB segments (MA 760) for a given grain aspect ratio. In the case of creep ductile CM 247 LC, it was shown that if there is alarge fraction of grains that are oriented for single slip, this results in higher creep rates and lower rupture times than if there is only a small fraction of such grains. The study of the influence of grain morphology on creep damage accumulation in the creep-brittle and notch-sensitive ODS alloy MA 760 showed that large scatter in creep rupture lives is related to (1) the stochastic nature of creep damage accumulation on transverse GB segments and (2) the spatial distribution of transverse GB segments. It is the combination of these two factors that results in increased scatter in rupture lives as compared to equiaxed fine grain structures.

Effect of Multiaxial Stresses on Creep Damage of 316 Stainless Steel Weldments
YU-HSIAN HSIAO, HONGYAN ZHANG, and GLENN S. DAEHN
The difference in creep strength between a base metal and a weld metal always produces a multiaxial stress state even if the macroscopic loading is uniaxial. In this study, weldments were formed between wrought 316 stainless steel and two types of 316 weld metals with slightly different creep properties and chemical compositions. Full-size 316 weldments, including base metal, heat-affected zone (HAZ) and welds, were creep tested at 650°C. The multiaxial stress distributions in full-size 316 weldments were simulated by the finite element method (FEM). Three stress parameters, namely, the maximum principal stress (MPS), the yon Mises effective stress (VMS), and the principal facet stress (PFS), were used to correlate the local multiaxial stresses with local creep damage distributions and failure lifetime. Metallographic examination and creep rupture data showed that the PFS parameter gave the best prediction of the creep damage distribution caused by the multiaxial stresses in 316 weldments. This approach may have application in the design, life prediction, and in-service evaluation of weldments.

The Inter-Relationship between Grain Boundary Sliding and Cavitation during Creep of Polycrystalline Copper
AKWASI AYENSU and TERENCE G. LANGDON
High-temperature creep tests were conducted on polycrystalline copper of commercial purity in order to investigate the inter-relationship between the extent and the rate of grain boundary sliding (GBS) and the development of internal cavitation. An image processing technique was used to provide quantitative information on the size and shape of the cavities formed over a range of stresses and at temperatures from 673 to 873 K. The results demonstrate that cavity development is inhomogeneous within any specimen, such that there is an increase in the level of cavitation in regions of higher local strain. It is shown by quantitative measurements that the total cavitated area increases at the faster sliding rates, but the number density of cavities decreases at the highest sliding rates because of cavity interlinkage. When interlinkage is taken into account, the results confirm that the overall level of cavitation is related to the occurrence of GBS.

Bridge Toughening Enhancement in Double-Notched MoSi2/Nb Model Composites
S.M. PICKARD and A.K. GHOSH
Single-ply composites containing both laminate and continuous Nb fiber reinforcement coated with Al2O3 debond coatings in an MoSi2 matrix are used as model systems for investigating bridge toughening concepts for various precrack configurations. When cracks are introduced symmetrically on either side of the ductile phase with zero crack offset spacing (S = 0), a minimum amount of energy is expended in plastic deformation and the local rupture process in the metal, as measured by the area of the force displacement curve in tension. For asymmetric precracks introduced on either side of the ductile reinforcement, as the offset spacing, S, was varied from 1 to 20 R (R being the ductile phase half-thickness), the overall extension continuously increased within the bridging ligament. The effective ligament gage length was nearly equal to the crack spacing in the limiting case of a weak interface. However, the ductile Nb phase developed a Nb5Si3 reaction layer on its surface which was strongly bonded to the Nb and was found to undergo periodic cracking, leading to numerous shear bands within the ductile phase. This unique and previously unreported mode of metal deformation in shear loading has been analyzed using a simple geometric model. The results indicate that the profusion of shear bands is the primary source of toughening enhancement in the case of asymmetric crack geometry, which was not recognized in prior work of this type.

ALLOY PHASES

Neutron Diffraction Study of Austempered Ductile Iron
C.S. CHOI, W. SHARPE, J. BARKER, and R.J. FIELDS
Crystallographic properties of an austempered ductile iron (ADI) were studied by using neutron diffraction. A quantitative phase analysis based on Rietveld refinements revealed three component phases, -Fe (ferrite), -Fe (austenite), and graphite precipitate, with weight fractions of 66.0, 31.5, nd 2.5 pct, respectively. The ferrite phases of the samples were found to be tetragonal, I 4/mmm, with a c/a ratio of about 0.993, which is very close to the body-centered cubic (bcc) structure. The austenite phase had C atoms occupying the octahedral site of the face-centered cubic (fcc) unit cell with about 8 pct occupancy ratio. A strong microstrain broadening was observed for the two Fe phases of the samples. The particle sizes of the acicular ferrite phase were studied by using small angle neutron scattering. The analysis suggested a mean rod diameter of 700Å. The scattering invariant predicts a ferrite volume fraction consistent with the powder diffraction analysis. A textbook case of nodular graphite segregation, with average diameters ranging from 10 to 20 µm, was observed by optical micrography.

Electron Microscope Study of Al-Fe-Si Intermetallics in 6201 Aluminum Alloy
M.H. MULAZIMOGLU, A. ZALUSKA, J.E. GRUZLESKI, and F. PARAY
The Al-Fe-Si intermetallics present in a commercial cast 6201 electrical conductor alloy have been studied using high resolution electron microscopy. The -Al5FeSi phase is highly faceted and contains multiple (001) growth twins parallel to the growth direction. The -Al8Fe2Si phase which forms in a Chinese script morphology has a nonfaceted interface with the aluminum matrix and exhibits no growth twinning. Formation of the phase is believed to occur via a peritectic decomposition of -Al8Fe2Si at 612°C. Observations made by transmission electron microscopy (TEM) support this hypothesis. When 30 ppm strontium is added to this alloy, the phase is stabilized and very little -Al5FeSi appears in the microstructure. A silicon-rich layer is found around the -phase particles. It is proposed that strontium adsorbs to the -phase interface, and in so doing, the diffusion of silicon into the phase, necessary for its transformation to , is prevented.

TRANSFORMATIONS

Ostwald Ripening in Ternary Alloys
C.J. KUEHMANN and P.W. VOORHEES
A theory of coarsening in an isothermal, ternary alloy is developed in an effort to understand the effects of a third chemical component on the ripening behavior of a two-phase system. The analysis is valid for a general, nonideal, nondilute solution, but is limited to extremely small volume fractions of the coarsening phase and neglects off-diagonal terms in the diffusion matrix. The Gibbs/Thompson equation in a ternary system undergoing coarsening reveals that the concentrations at the particle/matrix interface are dependent on the far-field supersaturations as well as on the particle radius. In addition, the capillary length depends on the diffusivities of the two components. An asymptotic analysis shows that the exponents of the temporal power laws for the average particle radius, number of particles per unit volume, and the matrix supersaturations are the same as that found in the binary limit; however, the amplitudes of the power laws are modified. We find that the trajectory of the matrix supersaturation must lie along a tie-line, but the trajectory of the particle composition does not. An expression for the effect of dilute ternary additions to the coarsening rate of a binary alloy is also given.

A New Characterization Method of the Microstructure Using the Macroscopic Composition Gradient in Alloys
TORU MIYAZAKI, TOSHIYUKI KOYAMA, and SENGO KOBAYASHI
A new experimental method to determine the phase boundary and phase equilibria is accomplished by using the transmission electron microscopic observation of alloys having the macroscopic composition gradient. The various phase boundaries, i.e., the coherent binodal and spinodal lines and incoherent binodal line, are distinctly determined for the Cu-Ti alloy system. Furthermore, the equilibrium compositions at the interface of precipitate/matrix are experimentally obtained for various particle sizes, and therefore, the Gibbs/Thompson relation is verified. It is expected that the composition gradient method proposed in the present study will become an important experimental method for microstructural characterization.

The Influence of Niobium Supersaturation in Austenite on the Static Recrystallization Behavior of Low Carbon Microalloyed Steels
E.J. PALMIERE, C.I. GARCIA, and A.J. DeARDO
This work describes the effect of Nb supersaturation in austenite, as it applies to the strain-induced precipitation potential of Nb(CN), on the suppression of the static recrystallization of austenite during an isothermal holding period following deformation. Four low carbon steels, microalloyed with Nb, were used in this investigation. Three of the steels had variations in Nb levels at constant C and N concentrations. Two steels had different N levels at constant C and Nb concentrations. The results from the isothermal deformation experiments and the subsequent measurement of the solution behavior of Nb in austenite show that the recrystallization-stop temperature (TRXN) increases with increasing Nb supersaturation in austenite. Quantitative transmission electron microscopy analysis revealed that the volume fraction of Nb(CN) at austenite grain boundaries or subgrain boundaries was 1.5 to 2 times larger than Nb(CN) volume fractions found within the grain interiors. This high, localized volume fraction of Nb(CN) subsequently led to high values for the precipitate pinning force (FPIN). These values for FPIN were much higher than what would have been predicted from equilibrium thermodynamics describing the solution behavior of Nb in austenite.

Communication: The Driving Force for Martensitic Transformations in Low Alloy Steels
V. RAGJAVAN AND DARA P. ANTIA

Communication: Modeling Iron Enrichment in Hot-Dip Galvanneal Coatings on Interstitial-Free Steels
P.R. RIOS

Modeling of Sequential Reactions during Micropyretic Synthesis
V. SUBRAMANIAN, M.G. LAKSHMIKANTHA, AND J.A. SEKHAR
A numerical model for a two-step sequential micropyretic reaction is reported. Such multiple reactions can take place during micropyretic synthesis of composite materials. The model was developed or the aluminothermic reaction between molybdenum oxide, aluminum, and silicon, which react to give molybdenum disilicide and aluminum oxide. The model was used to obtain the solution for the propagation of the combustion front. The melting of various constituents of reactants and products was incorporated into the model. The effect of the pre-exponential factor and the amount of diluent on the nature of propagation and temperature profile was investigated. Other conditions of propagation and synthesis for general two-step reactions were explored by changing the activation energy and heat release of each sequential reaction. A mapping procedure to characterize the types of sequential reactions is proposed and studied for several aluminothermic type reactions.

A Study on Morphology and Plate Mean Dimensions in Fe-Ni and Fe-Ni-Cr Alloys
P. VISVESVARAN
A systematic study has been carried out in Fe-Ni as well as Fe-Ni-Cr alloys to understand whether the factors related to the burst temperature or alloy composition are responsible for various morphologies as well as mean plate dimensions. A systematic procedure has been adopted to give a set of Fe-Ni-Cr alloys with constant transformation burst temperature (M). While maintaining the M constant, it is found that Cr replaces more and more Ni with further additions. The martensitic transformation progresses predominantly through a spreading-out process. The aspect ratio (c/r) follows a parabolic relation with M, whereas it is linear with respect to Ni content in the case of Fe-Ni alloys. In Fe-Ni-Cr alloys, the aspect ratio, however, does not show any relationship with composition at 133 K. The appearance of different morphologies and the variation in different features within a morphology are seen in alloys with different compositions having the same Mb.

TRANSPORT PHENONEMA

Sputter-Induced Pits on {100} Nickel Surfaces
J.K. STEELE AND D.I. POTTER
Nickel (Ni+) ions of 180 keV energy impinging on {100} faces of nickel single crystals produce sputtered surfaces. Examination of these surfaces exposed to fluences up to 8 x 1017 ions/cm2 and at temperatures between 25°C and 750°C reveals pits with facets parallel to the {111} and {100} crystallographic planes of the nickel. Subsurface voids also form and, when intersected by the sputtered surface, become small pits which grow with further sputtering. The pits exhibit facets that are direct extensions of facets present on the voids. The voids nucleate and grow during the initial stages of bombardment at temperatures above 600°C but shrink beyond fluences of ~l3.5 x 1017 ions/cm2. Voids are not observed after bombardment at temperatures less than 600°C. Sputtering at these lower temperatures produces no pits unless the nickel is bombarded first at higher temperatures to produce the requisite voids. Measuring the rate at which the {100} surface recedes due to sputtering provides the sputtering yield. This yield, near 3.8 atoms per Ni+ ion, is independent of temperature from 25°C to 750°C. The growth rate of the pits, i.e., the rate at which oppositely inclined {111} faces separate, is also measured. At temperatures below 350°C, the measured growth rate matches that based on sputtering of these inclined surfaces. The rate increases with increasing temperature above 350°C, reaching nearly tenfold its low-temperature value by 750°C. The mechanisms causing this accelerated growth with increasing temperature are discussed and related to the migration of the point defects produced by the bombardment.

MECHANICAL BEHAVIOR

The Bauschinger Effect in a SiC/Al Composite
R.J. ARSENAULT and U.T.S. PILLAI
An interesting mechanical property of SiC/Al composites is that the tensile yield stress is less than the compressive yield stress, even though the apparent modulus in tension is greater than that in compression. An investigation was undertaken to determine if the Bauschinger effect (BE) in a SiC/Al composite is asymmetrical. It was found that the BE is indeed asymmetrical in the case of the composite and the magnitude of the BE increases with total forward strain. These results can be explained in terms of the changes in ``back stress'' caused by the changes in the residual stress and the work hardening during forward strain.

High-Temperature Measurements of Lattice Parameters and Internal Stresses of a Creep-Deformed Monocrystalline Nickel-Base Superalloy
HORST BIERMANN, MARCUS STREHLER, and HAEL MUGHRABI
High-temperature X-ray line profile measurements were performed to maximal temperatures of 1050°C on samples of the nickel-base superalloy SRR 99. The samples with rod axes near the [001] direction were investigated in the initially undeformed state and after creep deformation at different temperatures and stresses. For the measurements of the (002) and (020) line profiles, a special X-ray double crystal diffractometer with negligible line broadening was used which was equipped with a high-temperature vacuum chamber. The line profiles were evaluated for the lattice parameters of the matrix phase and the precipitated ' phase and for values of the lattice mismatch parallel and perpendicular to the stress axis, respectively, which were found to be different. Elastic, tetragonal distortions of the phases and ' could be determined between room temperature and about 900°C. These distortions are thermally induced due to the different thermal expansion coefficients of the two phases and deformation induced due to interfacial dislocation networks which were built up during deformation. At the high temperatures of the X-ray measurements, at least partial recovery of the deformation-induced internal stresses occurred, depending on the temperature of the X-ray measurements. The results are discussed and compared with data obtained by complementary techniques.

The Embrittlement and De-Embrittlement of Grain Boundaries in an Fe-Mn-Ni Alloy Due to Grain Boundary Segregation of Mn
NAM-HOE HEO and HU-CHUL LEE
A ductile-brittle-ductile (DBD) transition behavior in an age-hardenable Fe-8Mn-7Ni alloy has been analyzed in light of segregation and desegregation of alloying elements at prior austenite grain boundaries. The DBD transition in the alloy can be distinguished by two C-type curves: one corresponding to the start of zero tensile elongation and the other to the finish. The activation energies for ductile-to-brittle and brittle-to-ductile transitions are in close agreement with that for age hardening. Manganese content at the prior austenite grain boundaries was analyzed by Auger electron spectroscopy, and intergranular fracture strength at the brittle fracture region showed inverse trends with Mn concentration at the grain boundaries. All these observations strongly suggest that manganese segregation and its desegregation are responsible for the DBD transition of this alloy.

Temperature Dependence of the Intrinsic Small Fatigue Crack Growth Behavior in Ni-Base Superalloys Based on Measurement of Crack Closure
M. OKAZAKI, H. YAMADA, and S. NOHMI
The effect of temperature on the small fatigue crack growth behavior of a single crystal and directionally solidified Ni-base superalloys was investigated at temperatures between 873 to 1123 K by measuring the crack closure. The results were also compared with those of the physically long crack. It was found that the propagation resistance and the fatigue threshold of the long cracks increased with temperature in all the materials. The long crack growth rates at three temperatures were approximately represented by an unique curve, after taking account of crack closure level and elastic modulus. In contrast, the small crack growth resistance decreased with temperature even when the crack closure phenomenon was taken into consideration. Furthermore, the small fatigue cracks exhibited considerably higher growth rates than the long cracks at a given effective stress intensity actor range and also grew under effective stress intensity factor ranges below the long crack threshold. The factors responsible for the lack of similitude in propagation rates between small and long cracks were also discussed, based on these observations and the chemical analysis near the crack tip using the electron probe microanalyzer.

Identification of Precipitate Phases in a Mechanically Alloyed Rapidly Solidified Al-Fe-Ce Alloy
M.L. OVECOGLU, C. SURYANARAYANA, and W.D. NIX
The stable and metastable precipitate phases which form during mechanical alloying of a rapidly solidified (RS) Al-8.4Fe-3.4Ce alloy have been unambiguously identified using X-ray diffraction, transmission electron microscopy (TEM), and energy dispersive spectroscopy techniques. The metastable Al10Fe2Ce and stable Al13Fe3Ce and Al13Fe4 intermetallic phases, with crystal structures and lattice parameters as reported in the literature, have been identified. It is shown that the metastable Al10Fe2Ce intermetallic phase particles have elongated shapes and their sizes range between 100 and 200 nm and are free of any localized faults, whereas the equilibrium Al13Fe3Ce and Al13Fe4 intermetallic phases are equiaxed in shape and have particle sizes ranging from 200 to 500 nm. It is suggested that the presence of the metastable Al10Fe2Ce in this material is due to its incomplete transformation to the equilibrium Al13Fe3Ce phase.

Micronecking and Fracture in Cavitated Superplastic Materials
MOHAMED ZAKI
A model of cavity growth is used to describe neck development in the ligament between voids and fracture strain of cavitated superplastic materials. The results show that the strain-rate sensitivity index has an important effect on fracture strain only at low values of cavity growth rate. This is more appreciable for a lesser initial cavitation level. The initial cavitation level weakly influences the fracture strain, in contrast to the result for the cavity growth rate. It is seen that the present fracture criterion fits well the experimental results for several superplastic materials.

Friability and Crushing Strength of Micrometer-Size Diamond Abrasives Used in Microgrinding of Optical Glass
YIYANG ZHOU, TOSHIO TAKAHASHI, DAVID J. QUESNEL, and PAUL D. FUNKENBUSCH
In abrasive grinding, the properties of the abrasives and their response to impact loading play a significant role in determining the results achievable. For micrometer-size diamond abrasives used for bound-abrasive microgrinding of optical glass, friability testing is used to estimate the related particle properties. Friability and crushing strength of diamond abrasives are estimated based on the data from comminution of sample powders on a commercial SPEX mixer/mill. Different diamond abrasives as well as a CBN abrasive are tested. Evolution of powder size and size distribution with comminution time is characterized with a HORIBA laser scattering analyzer. Correlation is established for the impact stress and the probability of fracture during comminution. This study demonstrates how to combine the ease of data acquisition found in a conventional friability test with the capability of predicting specific mechanical properties normally found only by crushing individual abrasive particles.

PHYSICAL CHEMISTRY

Thermodynamics and Long-Range Order of Nitrogen in '-Fe4N1-x
BART J. KOOI, MARCEL A.J. SOMERS, and ERIC J. MITTEMEIJER
Models are given for the description of the chemical potential of nitrogen in '-Fe4N1-x. In previous work, '-Fe4N1-x was treated as a (sub)regular solution, thereby assuming that the N atoms are distributed randomly on the sites of their own sublattice. However, in '-Fe4N1-x, long-range ordering occurs of the N atoms over the sites of their own sublattice. Then, the expression for the configurational entropy should account for the occurrence of ordering. In the present article, the descriptions adopted and tested for '-Fe4N1-x are based on a Langmuir-type approach, the Wagner/Schottky (WS) approach, and the Gorsky/Bragg/Williams (GBW) approach. Application of the various models to data of nitrogen-absorption isotherms for the ' iron-nitride phase shows that the subregular solution concept fails to describe the experimental data satisfactorily, whereas a very good agreement between theory and experiment is obtained for the WS and GBW approaches. It is shown that, in particular, accounting for the occupation of disorder (octahedral) sites by N atoms is necessary to obtain an accurate description of the chemical potential of nitrogen in '-Fe4N1-x.

An Evaluation of the Fe-N Phase Diagram Considering Long-Range Order of N Atoms in '-Fe4N1-x and -Fe2N1-z
BART J. KOOI, MARCEL A.J. SOMERS, and ERIC J. MITTEMEIJER
The chemical potential of nitrogen was described as a function of nitrogen content for the Fe-N phases -Fe[N], '-Fe4N1-x, and -Fe2N1-z. For -Fe[N], an ideal, random distribution of the nitrogen atoms over the octahedral interstices of the bcc iron lattice was assumed; for '-Fe4N1-x, and -Fe2N1-z, the occurrence of a long-range ordered distribution of the nitrogen atoms over the octahedral interstices of the close packed iron sublattices (fcc and hcp, respectively) was taken into account. The theoretical expressions were fitted to nitrogen-absorption isotherm data for the three Fe-N phases. The / + ', + + '/', '/' + and ' + / phase boundaries in the Fe-N phase diagram were calculated from combining the quantitative descriptions for the absorption isotherms with the known composition of NH3/H2 gas mixtures in equilibrium with coexisting and ' phases and in equilibrium with coexisting ' and phases. Comparison of the present phase boundaries with experimental data and previously calculated phase boundaries showed a major improvement as compared to the previously calculated Fe-N phase diagrams, where long-range order for the nitrogen atoms in the ' and phases was not accounted for.

SURFACE TREATMENT

Theoretical Treatment of Nitriding and Nitrocarburizing of Iron
HONG DU and JOHN AGREN
Mathematical models are developed for both nitriding and nitrocarburizing of iron taking into account the diffusion of N or C and N through various phases and the thermodynamic properties of the ternary Fe-C-N system. Analytical solutions are obtained for the /' bilayer growth of the compound layer assuming constant diffusion coefficients, and the results are compared with those obtained from numerical simulations taking into account the concentration-dependent diffusivities. No significant difference was found between these two methods for nitriding of iron. For nitrocarburizing of iron, it was found that the off-diagonal diffusivities of the and ' phases must be taken into account in the analytical solution in order to obtain reasonable results. In addition, it is shown that the phase constitution of the compound layer produced during nitrocarburizing of iron can be predicted by the numerical simulation.

SOLIDIFICATION

The Breakdown of Single-Crystal Solidification in High Refractory Nickel-Base Alloys
T.M. POLLOCK and W.H. MURPHY
The breakdown of single-crystal solidification has been studied over a wide range of solidification conditions in ten superalloys with large variations in Re, Ta, and W content. Over the range of experimental conditions investigated, grain defect formation was sensitive to local thermal and solutal conditions. For a fixed alloy composition and withdrawal rate, the transition from single-crystal to equiaxed solidification did not occur abruptly. Instead, as thermal gradients were decreased in a series of experiments, isolated, highly misoriented columnar grains with the same composition as that of the base alloy developed in the presence of positive (stabilizing) thermal gradients with increasing frequency until the advance of the single-crystal front was completely blocked. The onset of columnar grain formation occurred when the primary dendrite arm spacing exceeded a critical value, corresponding to a morphological transition in the dendritic array. The onset of ``freckling'' was observed at the same primary dendrite arm spacing where misoriented columnar grains began to appear. In experiments with varying levels of refractory alloy content, there was also a strong correlation between the onset of grain formation and freckle formation. These observations strongly suggest that in high refractory content superalloys, the breakdown of single-crystal solidification and the formation of misoriented grains as well as freckle-type defects are sensitively dependent on thermosolutal convection processes.

Convection during Thermally Unstable Solidification of Pb-Sn in a Magnetic Field
H. SONG, S.N. TEWARI, and H.C. de GROH III
Convection and macrosegregation in directionally solidified hypoeutectic Pb-38 wt pct Sn and hypereutectic Pb-64.5 wt pct Sn have been examined during upward and downward growth. Temperature fluctuations are observed along the length of the melt column during downward growth. With increasing Rayleigh number, these fluctuations change from none, to cyclic, to time periodic having multiple harmonics, and finally to random. At the higher convective driving force of 350 K temperature inversion, the transverse magnetic field decreased convective levels, strong random temperature fluctuations (flows) becoming smaller and periodic. The maximum field of 0.45 T was unable to completely eliminate convection. For the lower convective driving force of 150 K temperature inversion, the 0.05 T magnetic field decreased flows, and at 0.15 T, the field caused a dramatic decrease in the characteristic frequency of the temperature fluctuations, indicating a change in the nature of the flow, the waveform of the temperature fluctuations changing from sinusoidal to a pulsed wave. Temperature fluctuations and time delays between thermocouples were used to estimate flow velocities. Irrespective of the convection in the bulk melt (ahead of the mushy zone), longitudinal macrosegregation occurs only if the interdendritic melt mixes with the bulk melt.

Time Dependence of Tip Morphology during Cellular/Dendritic Arrayed Growth
H. SONG and S.N. TEWARI
Succinonitrile-1.9 wt pct acetone has been directionally solidified in 0.7 x 0.7-cm-square cross section pyrex ampoules in order to observe the cell/dendrite tip morphologies, not influenced by the ``wall effects,'' which are present during growth in the generally used thin (about 200 µm) crucibles. The tips do not maintain a steady-state shape, as is generally assumed. Instead, they fluctuate within a shape envelope. The extent of fluctuation increases with decreasing growth speed, as the microstructure changes from the dendritic to cellular. The influence of natural convection has been examined by comparing these morphologies with those grown, without convection, in the thin ampoules.

MATERIALS PROCESSING

Microstructure and Phase Relations in a Powder-Processed Ti-22Al-12Nb Alloy
S.G. KUMAR and R.G. REDDY
A systematic investigation was undertaken to compare the effect of processing on the phase relations and microstructure of 66Ti-22Al-12Nb (in at. pct) alloy. The alloy was processed by three different routes: (1) cold pressing (CP) followed by reaction sintering; (2) CP followed by hot pressing (HP) followed by sintering; and (3) arc melting (AM), hydride-dehydride processing to make the alloy powder followed by cold isostatic pressing and then sintering. The samples were analyzed by X-ray diffraction (XRD); optical microscopy, scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS), and electron microprobe analysis (EPMA). The analyses showed that all the processing methods have resulted in the same phases, but the AM route resulted in an equiaxed microstructure, whereas the other two methods resulted in a lamellar microstructure. This refinement in microstructure was attributed to the hydride-dehydride processing step of the AM route.

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