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Volume 28A, No. 11, November 1997 This Month Featuring: Alloy Phases; Transformations; Mechanical Behavior; Environment; Welding & Joining; Solidification; Materials Processing; Composite Materials. View November 1997 Contents.
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' phase of the type Ni3Al. The partial pressures of Al, Co, and Ni were determined over the samples investigated. Excess chemical potentials at a temperature of 1473 K resulted for the components in the ' solubility range. New results on the phase boundaries of the ' solubility lobe were obtained by the analysis of quenched alloy samples and from the mass spectrometric studies. The results obtained are discussed with respect to the solubility behavior of Co in the ' phase.
The Evolution of Solutions: A Thermodynamic Analysis of Mechanical Alloying
A.Y. BADMOS and H.K.D.H. BHADESHIA
Normal thermodynamic theory for solutions begins with the mixing of component atoms. Many solutions are, however, prepared by mixing together lumps of the components, each of which might contain millions of identical atoms. We examine here the way in which a solution evolves from these large clusters of components, from a purely thermodynamic point of view. There are some interesting results, including the prediction that solution formation by the mechanical alloying of solid components cannot occur unless there is a gain in coherency as the particles become small. The nature of the barrier to mechanical alloying is discovered. There is also the possibility of a metastable state prior to the achievement of full solution, when the component atoms prefer like-neighbors.
Effect of Carbon and Nitrogen on Chemical Homogeneity of Fcc Iron-Based Alloys
V.G. GAVRILJUK, A.L. SOZINOV, A.G. BALANYUK, S.V. GRIGORIEV, O.A. GUBIN, G.P. KOPITSA, A.I. OKOROKOV, and V.V. RUNOV
Iron-based fcc alloys containing (at. pct) 18 Cr, 15Ni, 10Mn and 18Cr, 15Ni were additionally alloyed with either carbon or nitrogen and studied by the small angle scattering of thermal polarized neutrons. Carbon and nitrogen were found to influence neutron scattering in opposite ways. An increase in carbon content enhances the inhomogeneity of the solid solution on a scale that significantly exceeds the lattice parameter. Nitrogen, on the contrary, slightly decreases the inhomogeneity of FeCrNiMn and FeCrNi austenites. The data obtained are discussed in terms of short-range atomic order and enable one to clarify the physical reason for differences in the thermodynamical stability of multicomponent iron-based fcc solid solutions alloyed with either carbon or nitrogen, which is important for the development of high-strength corrosion-resistant alloys.
(bcc) and the product 
(hcp) or -hydride (fct) phases are remarkably similar for different types of transfor mations. Crystallographic features such as orientation relations, habit planes, and interface structures associated with these transformations have been compared, with a view toward examining whether the transformation mechanisms have characteristic imprints on these experimental observables. Martensites exhibiting dislocated lath, internally twinned plate, and self-accommodating three-plate cluster morphologies have been encountered in Zr-2.5Nb alloy. Habit planes corresponding to all these morphologies have been found to be consistent with the predictions based on the invariant plane strain (IPS) criterion. Different morphologies have been found to reflect the manner in which the neighboring martensite variants are assembled. Lattice-invariant shears (LISs) for all these cases have been identified to be either {
} <
> slip or twinning on {} planes. Widmanstätten precipitates, forming in a step-quenching treatment, have been shown to have a lath morphology, the / interface being decorated with a periodic array of <c + a> dislocations at a spacing of 8 to 10 nm. The line vectors of these dislocations are nearly parallel to the invariant lines. The precipitates, forming in the retained phase on aging, exhibit an internally twinned structure with a zigzag habit plane. Average habit planes for the morphologies have been found to lie near the {103} - {113} poles, which are close to the specific variant of the {112} plane, which transforms into a prismatic plane of the type {
}. The crystallography of the formation of the -hydride phase (fct) from both the and phases is seen to match the IPS predictions. While the - transformation can be treated approximately as a simple shear on the basal plane involving a change in the stacking sequence, the - transformation can be conceptually broken into a 
transformation following the Burgers correspondence and the simple - shear process. The active eutectoid decomposition in the Zr-Cu system, + ', has been described in terms of cooperative growth of the phase from the phase through the Burgers correspondence and of the partially ordered ' (structurally similar to the equilibrium Zr2Cu phase) through an ordering process. Similarities and differences in crystallographic features of these transformations have been discussed, and the importance of the in variant line vector in deciding the geometry of the corresponding habit planes has been pointed out.
Evolution of Recrystallization Texture from Aluminum Sheet Cold Rolled under Unlubricated Condition
CHANG-HEE CHOI and DONG NYUNG LEE
The texture of cold-rolled aluminum sheet has been known to vary through thickness due to inhom ogeneous deformation, which can be caused by a characteristic deformation zone geometry and friction between materials and rolls during rolling. The copper texture is obtained in the center layer, which is plane strain compressed, while the shear texture is in the surface layer, which is approximated by major {001}<110> and minor {111}<112> and {111}<110> components. The recrystallization texture of the surface layer is approximated by {225}<10 5 2>. The evolution of the recrystallization texture has been explained by the maximum energy release theory, in which the absolute maximum normal stress direction in the deformed state becomes parallel to the minimum elastic modulus direction of the recrystallized grains.
Synthesis of Nanodispersed Phases during Rapid Solidification and Crystallization of Glasses in Ti75Ni25 Alloys
R. NAGARAJAN, K. AOKI, and K. CHATTOPADHYAY
The formation of the metallic glass and crystalline phases and related microstructures and the decomposition behavior of rapidly solidified Ti75Ni25 alloys obtained under different processing conditions have been investigated in detail. The competition between glass transition and nucleation of -Ti during rapid solidification leads to the possibility of synthesizing the nanocomposites of -Ti and glass. Additionally, it is shown that the presence of a small amount of Si also promotes simultaneous nucleation of fine Ti2Ni intermetallic compound. Thermodynamic calculation of the metastable phase diagram indicates the presence of a metastable eutectic reaction between -Ti and Ti2Ni. Evidence of this reaction at lower cooling rates has been presented. On heating, the glass decomposes through this reaction. Finally, on the basis of understanding of the microstructural evolution during decomposition, a new approach has been adopted to synthesize a nanodispersed composite of -Ti in the crystalline Ti2Ni matrix with a narrow size distribution by controlling the devitrification heat treatment of the metallic glass.
Communication: Development of Reproducible and Increased Strength Properties in Thick Extrusions of Low-Alloy Al-Zn-Mg-Cu Based AA 7075
A.K. MUKHOPADHYAY
Communication: Discussion of "Kinetics and Phase Transformation Evaluation of Fe-Zn-Al Mechanically Alloyed Phases"
NAI-YONG TANG
Authors' Reply
OSWALD N.C. UWAKWEH and ZHENTONG LIU
Damage Effect on the Fracture Toughness of Nodular Cast Iron: Part I. Damage Characterization and Plastic Flow Stress Modeling
M.J. DONG, C. PRIOUL, and D. FRANÇOIS
After chemical, morphological, and mechanical characterization of ductile cast iron, the damage mechanisms were studied by tensile tests inside the scanning electron microscope (SEM). The evolutions of Young's modulus and of Poisson's ratio were measured in uniaxial tensile tests. Compression tests were used to measure the pressure sensitivity coefficient of the flow stress. The damage is produced by early initiation of cavities at the pole cap of graphite nodules by debonding of the interface, followed by the growth of cavities. The mechanical behavior was modeled in the elastic region by calculating the Hashin-Shtrickman bounds. This provided the elastic constants for the graphite nodules. The plastic behavior was modeled by considering that the graphite nodules were replaced by voids. The critical interfacial stress for debonding was determined by analytical as well as by finite-element calculations. The growth rate of cavities was deduced from the evolution of the Poisson's ratio and was compared with predictions from Gurson's potential. The stress-strain behavior could be modeled either by extension of the Mori-Tanaka analysis in the plastic range or by finite-element computations. This allowed a fair prediction of the observed behavior.
Damage Effect on the Fracture Toughness of Nodular Cast Iron: Part-II. Damage Zone Characterization ahead of a Crack Tip
M.J. DONG, C. PRIOUL, and D. FRANÇOIS
In order to understand the fracture toughness of nodular cast iron, the damage zone was studied by Scanning Electron Microscope (SEM) observations of the polished surface of a CT 25 specimen before and after ductile tearing. Damage is defined as decohesion at the graphite/matrix interface. It is shown that the damage zone is very large in nodular cast iron (almost throughout the whole remaining ligament ahead of the crack tip), so linear elastic fracture mechanics (LEFM) are not valid for small specimens. The size of the damage zone was calculated analytically by introducing a damage initiation criterion which was based both on observations of the debonding of the interface between matrix and graphite nodules and on measurements of the pressure sensitivity of cast iron. To take into account the actual boundary conditions, the damage zone was also calculated by numerical modeling using the modified Gurson's model and by considering the nodular cast iron as a porous material. The calculated results led to good agreement with the damage zone observations. Plane stress and plane strain calculations yielded nearly the same size plastic zone. This result is opposite to those obtained for fully dense materials.
Contact of Crack Surfaces during Fatigue: Part I. Formulation of the Model
ANA MARÍA GARCÍA and HUSEYIN SEHITOGLU
A model has been developed to predict crack opening and closing behavior for propagating fatigue cracks which undergo significant sliding displacements at crack flanks. Crack surfaces were described statistically by assuming a random distribution of asperity heights and a mean density of asperities and asperity radii. The propagating crack was subdivided into strips, and each strip was treated as a contact problem between two randomly rough surfaces. The remote tensile stresses were varied in a cyclical manner. The contact stresses at minimal load were determined by analyzing the local crushing of asperities via a sliding mechanism. Then, upon loading, the crack opening stress levels were computed when the contact stresses were overcome. Part I of this article includes a discussion of the previous models, then introduces statistical contact mechanics concepts which are utilized in the fatigue crack growth simulations. In addition, the numerical algorithms for the modeling work and the sensitivity of results to model parameters are described. The role of stress ratio, maximum stress level, crack length, and the geometry of crack surfaces on the crack growth behavior will be discussed in Part II of this article.
Contact of Crack Surfaces during Fatigue: Part II. Simulations
HUSEYIN SEHITOGLU and ANA MARÍA GARCÍA
A detailed model of the role of asperities in crack closure has been initiated in Part I of this article. Crack opening stress is defined as the far-field stress required to overcome the asperity-induced contact stresses along the crack. In this Part II, the magnitude of crack opening stress is established as a function of roughness (
0); asperity density (N); maximum stress level (Smax/Sy); shakedown pressure (ps0/k), which reflects the effect of tangential tractions or friction; R ratio; and crack length. Normalizations permit application to a wide range of materials. The results, for selected levels of asperity density, are consolidated upon comparing the crack opening displacement (COD) with the roughness (0) over four orders of magnitude. Specifically, a nonlinear relationship between COD/0 and crack opening stress was established that can be readily used to determine crack opening stress over a broad range of conditions. The model has been utilized to predict crack opening stress levels for several materials, including 0.8 pct C steels, 9Cr-1Mo steels, Ti-4Al, Ti-46Al (-aluminide), and Al 2124 alloys. Experimental measurements of crack roughness and asperity density were conducted on titanium aluminide specimens using confocal microscopy, and crack closure predictions were made with the model. The predictions demonstrated very good agreement with the experimentally measured closure levels.
Effect of Impurity Hydrogen on the Deformation and Fracture in an Al-5 Mass Pct Mg Alloy
GOROH ITOH, TAKESHI JINKOJI, MOTOHIRO KANNO, and KATSUMI KOYAMA
Air-melted and argon-melted Al-5 mass pct Mg alloy specimens containing impurity hydrogen of 0.27 and 0.04 mass ppm, respectively, were tensile-tested at ambient temperature. The ductility and fracture processes were compared in the two specimens, and hydrogen evolution behavior during the test was also compared using a special testing machine equipped with a mass spectrometer and ultra high vacuum chamber. The air-melted specimen, containing a higher amount of hydrogen, had less reduction in area (RA) and a higher amount of evolved hydrogen gas on fracture. This implied that the impurity hydrogen was in the transgranular voids, which appeared as dimples on the fracture surface. Fracture process analysis involving fractography, load-displacement curve analysis, and op tical microscopy on a cross section of the deformed test piece demonstrated that the impurity hydrogen reduces nonuniform elongation by accelerating the nucleation of transgranular voids produced under triaxial tensile stress after necking. Hydrogen evolution was also detected corresponding to each load drop in the serrated flow of the air-melted specimen, supporting the idea that hydrogen atoms are transported with moving dislocations.
Effects of Test Temperature, Grain Size, and Alloy Additions on the Low-Temperature Fracture Toughness of Polycrystalline Niobium
A.V. SAMANT and J.J. LEWANDOWSKI
The current work investigates the effects of test temperature (77 to 150 K), grain size (63 to 165 µm), and solid solution alloying additions of zirconium (Zr) on the fracture toughness (Kq, KIc) of polycrystalline niobium (Nb). Extensive fracture surface analyses of the fractured specimens revealed the location of the apparent cleavage fracture nucleation sites. Comparisons have been made to models for cleavage fracture toughness as well as to predictions of the peak stress locations using existing finite element models for a crack loaded under plane strain conditions.
Plastic-Flow and Microstructure Evolution During Hot Deformation of a Gamma Titanium Aluminide Alloy
V. SEETHARAMAN and S.L. SEMIATIN
The hot workability of a near gamma titanium aluminide alloy, Ti-49.5Al-2.5Nb-1.1Mn, was assessed in both the cast and the wrought conditions through a series of tension tests conducted over a wide range of strain rates (10-4 to 100 s-1) and temperatures (850°C to 1377°C). Tensile flow curves for both materials exhibited sharp peaks at low strain levels followed by pronounced necking and flow localization at high strain levels. A phenomenological analysis of the strain rate and temperature dependence of the peak stress data yielded an average value of the strain rate sensitivity equal to 0.21 and an apparent activation energy of ~411 kJ/mol. At low strain rates, the tensile ductility displayed a maximum at ~1050°C to 1150°C, whereas at high strain rates, a sharp transition from a brittle behavior at low temperatures to a ductile behavior at high temperatures was noticed. Dynamic recrystallization of the gamma phase was the major softening mechanism controlling the growth and coalescence of cavities and wedge cracks in specimens deformed at strain rates of 10-4 to 10-2 s-1 and temperatures varying from 950°C to 1250°C. The dynamically recrystallized grain size followed a power-law relationship with the Zener-Hollomon parameter. Deformation at temperatures higher than 1270°C led to the formation of randomly oriented alpha laths within the gamma grains at low strain levels followed by their reorientation and evolution into fibrous structures containing + phases, resulting in excellent ductility even at high strain rates.
Influence of Limit Stress States and Yield Criteria on the Prediction of Forming Limit Strains in Sheet Metals
W.M. SING, K.P. RAO, and K. SWAMINATHAN
Several researchers have proposed analytical methods for predicting the forming limit curve (FLC), which has been successfully used as a diagnostic tool in sheetmetal forming. However, these approaches lack ease of adaptability to various situations and also involve considerable complexity. Sing and Rao proposed a new FLC modeling approach based on limit stress states derived from yield criterion and material properties from a simple tensile test. The first aspect of this study ad dresses the influence of the shape of the forming limit stress curve (FLSC) upon the FLC. The FLC modeled from a singly linear FLSC exhibits good agreement with the experimental curve, unlike those modeled from an elliptical or a piecewise linear FLSC. It is, thus, established that a linearized limit stress locus describes adequately the actual localized neck condition for the materials chosen in this study. Second, the study focuses on the suitability of the different cases of Hill's yield criterion for satisfactory prediction of FLCs. The FLCs predicted using different cases of Hill's criterion are compared with experimental FLCs in the case of steel and copper. Different cases of Hill's criterion provide a wider choice for FLC modeling for different classes of materials. The sensitivity of Hill's stress exponent is also thoroughly explored for achieving a close correspondence between the predicted and experimental FLCs.
Effect of Grain Size on the Observed Pseudoelastic Behavior of a Cu-Zn-Al Shape Memory Alloy
M. SOMERDAY, R.J. COMSTOCK, JR., and J.A. WERT
The shape of stress-strain curves for a pseudoelastic copper-based shape memory alloy (SMA) has been found to depend strongly on the grain size-to-sample thickness ratio (gs/t). Previous investigators have attributed this effect to reduced grain constraint in coarse-grain samples. The present investigation further analyzes the grain constraint effect by modeling shape memory alloy stress-strain curves. The model results reveal that varying grain constraint can explain the observed grain size effect on stress-strain curves. Furthermore, detailed consideration of the Taylor factor equivalent for Cu-Zn-Al and NiTi shape memory alloys can explain the opposite curvature of polycrystal stress-strain curves for these two materials. Finally, several indices of grain constraint are analyzed for the Cu-Zn-Al alloy examined in the present investigation and for similar alloys used in previous studies. This evaluation reveals that both transformation modulus and transformation stress correlate with gs/t, and each can be used as an index of grain constraint.
Modeling of Rolling Texture Development in a Ferritic Chromium Steel
L.S. TÓTH, A. MOLINARI, and D. RAABE
The development of crystallographic texture during rolling of a ferritic chromium steel containing 11 pct Cr was examined experimentally as well as by polycrystal modeling at large strains (up to 90 pct thickness reduction). The initial shape of the grains was very much elongated in the direction of rolling. A strong rolling direction (RD) fiber (<110> parallel to the rolling direction) has been observed at large strains in the experiment. The Taylor viscoplastic model, the relaxed-constraints pancake model, and the self-consistent viscoplastic approach were employed to simulate the texture development. Strain hardening was accounted for by microscopic hardening laws, for which the parameters were obtained from uniaxial tensile tests. It has been found that among the three models considered, the self-consistent viscoplastic model (the version tuned to finite-element results) yielded the best agreement with the experimentally observed texture evolution. Strong effects of grain shape and hardening have been found. The pancake model was also able to reproduce the main characteristics of the texture because of the flattened initial grain shape.
Latent Hardening Behavior of Monocrystalline Al-Mg Solid Solution
HSIN-MING WU, MAREK A. PRZYSTUPA, and ALAN J. ARDELL
The latent hardening behavior of dilute Al-Mg single crystal was investigated in this study. We performed the latent hardening tests on five systems, one in each of the five system groups. The latent hardening ratios (LHR) and the hardening rates were calculated. The LHR of systems that form attractive junctions is highest in this investigation. The LHRs of systems that form Lomer-Cottrell sessile locks, Hirth locks, or cross-slip systems are in the middle range. The coplanar system has the lowest LHR, which is in agreement with the theoretical prediction. An equation was devel oped that correlates the LHR with the dislocation densities at various prestrain values. The secondary deformation curve is predicted qualitatively in accordance with the interaction strength of the latent system with the primary system. Based on such a model, a prediction of the shapes of the secondary deformation curves in the strongest and weakest latent systems can be made.
Retained Austenite Characteristics in Thermomechanically Processed Si-Mn Transformation-Induced Plasticity Steels
A. ZAREI HANZAKI, P.D. HODGSON, and S, YUE
It is well known that a significant amount of retained austenite can be obtained in steel containing high additions (>1 pct) of Si, where bainite is the predominant microconstituent. Furthermore, retained austenite with optimum characteristics (volume fraction, composition, morphology, size, and distribution), when present in ferrite plus bainite microstructures, can potentially increase strength and ductility, such that formability and final properties are greatly improved. These beneficial properties can be obtained largely by transformation-induced plasticity (TRIP). In this work, the effect of a microalloy addition (0.035 pct Nb) in a 0.22 pct C-1.55 pct Si-1.55 pct Mn TRIP steel was investigated. Niobium was added to enable the steel to be processed by a variety of thermomechanical processing (TMP) routes, thus allowing the effects of prior austenite grain size, austenite recrystallization temperature, Nb in austenite solid solution, anti Nb as a precipitate to be studied. The results, which were compared with those of the same steel without Nb, indicate that the retained austenite volume fraction is strongly influenced by both prior austenite grain size and the state of Nb in austenite. Promoting Nb(CN) precipitation by the change in TMP conditions resulted in a decrease in the VRA. These findings are rationalized by considering the effects of changes in the TMP conditions on the subsequent transformation characteristics of the parent austenite.
The Influence of Austenite Grain Size and its Distribution on Chip Deformation and Tool Life during Machining of AISI 304L
LAIZHU JIANG, ÅKE ROOS, and PING LIU
In this article, the influence of austenite grain size and its distribution on chip deformation and tool life during machining of AISI 304L austenitic stainless steel bar is examined. Hot-forged bar and the quenched bars (at different quenching temperatures, 1050°C, 1100°C, 1150°C, and 1200°C) are machined at a high cutting speed. It was noted that the inhomogeneous distribution of grain size in the surface area, within a depth of 15 mm of the workpiece, resulted in tool edge breakage and lower tool life when machining the hot-forged bar compared with all of the quenched bars. In addition, a slight decrease in tool life was observed as the grain size increased in the quenched bars. The chip studies revealed that a higher segment height ratio of chip was gained when machining the hot-forged bar, compared to machining the quenched bars, due to the inhomogeneous distribution of grain size. Moreover, the thickness of the secondary shear zone was reduced as the grain size in creased. Interestingly, it was noticed that the chip work hardened during the machining process due to strain-induced twinning and 
martensite transformation. The studies of tool wear and failure revealed that a crack was initiated on the flank face at the interface between the deposited workpiece and the tool substrate when machining the hot-forged bar. This crack was formed due to either the thermal and mechanical fatigue or plastic deformation of the tool substrate. The fatigue crack propagated into the tool substrate through the decohesion of interface between carbides. The criterion of tool life when machining all of the quenched bars was normal flank wear. Based on the studies of chip deformation and the mechanisms for tool wear and failure, the effects of austenite grain size and its distribution on tool life were explained.
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