The role of twinning in the cavitation erosion of cobalt single crystals

The deformation characteristics contributing to the superior cavitation erosion properties of HCP cobalt single crystals have been determined. Results indicate that its erosion response is highly orientation sensitive. A homogeneous distribution of and glide occurs in {0110} crystals, whereas slip in the (0001) crystals is much more heterogeneous and consists mainly of dislocations. Continued exposure to cavitation nucleates a large number of twins, predominantly on the and planes in the and (0001) crystals respectively. The former twins are finer and more needle-like than the latter. The crystals are also significantly more erosion resistant than the (0001) crystals. The twin density increases continuously with cavitation exposure until a dense network of twins spans the entire exposed area. This fine-scale twinning is considered responsible for the superior erosion resistance of the metal.     

Twins as barriers to basal slip in hexagonal-close-packed metals

The boundary structure of {10 1}, {10 2}, {11 1} and, {11 2} twins in hexagonal-close-packed (hcp) metals and the interaction of crystal dislocations with the first two twin types have been studied previously using atomic-scale computer simulation. The interaction of crystal dislocations with {11 1} and {11 2} twin boundaries is described here and compared with the results for {10 1} and {10 2} twins. These four twins are found to create barriers to the motion of crystal dislocations gliding on the basal plane, and the strength of the barrier depends in a relatively complex manner on crystallographic parameters and details of the atomic structures of the interfaces. In some circumstances, crystal dislocations can be transmitted through the twin boundary, thereby creating twinning dislocations. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Competition among basal,prism, and pyramidal slip modes in hcp metals

The competition of slip among , and slip modes of hcp metals has been analyzed geometrically in terms of a critical resolved shear stress, CRSS, criterion. Under the action of an applied stress slip systems of one or more modes may be activated depending on the value of the CRSS and on the orientation of the slip systems with respect to the applied stress. If the CRSS of a given slip mode should exceed a limiting value relative to the CRSS of the other modes, however, the given mode becomes inoperative even under the most favorably stressed conditions. It is found by an examination of the yield loci that basal slip is inoperative if α₂ < cos θ; prism slip is inoperative if α₂ < α₁ sin θ; and pyramidal slip is inoperative if α₂ > cos θ + α₁ sin θ where and are, respectively, the ratios of CRSS for prism and pyramidal slips relative to basal slip, and ϕ is the angle between the (0001) and normals. Since the value of ϕ is a function ofc/a, the limiting values of α₁ and α₁ depend on thec/a ratio of the crystal structure.     

Twins as barriers to basal slip in hexagonal-close-packed metals

The boundary structure of , , , and twins in hexagonal-close-packed (hcp) metals and the interaction of crystal dislocations with the first two twin types have been studied previously using atomic-scale computer simulation. The interaction of crystal dislocations with and twin boundaries is described here and compared with the results for and twins. These four twins are found to create barriers to the motion of crystal dislocations gliding on the basal plane, and the strength of the barrier depends in a relatively complex manner on crystallographic parameters and details of the atomic structures of the interfaces. In some circumstances, crystal dislocations can be transmitted through the twin boundary, thereby creating twinning dislocations. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Multiphase binary diffusion in infinite and semi-infinite media: Part I. On the determination of interdiffusion coefficients

Mathematical relationships describing the multiphase binary diffusions are deduced under the condition that in an infinite medium, and also under the condition that and the fluxes of both the species occur in each other’s opposite direction through the surface in a semi-infinite medium, where are the interdiffusion coefficient and the partial molal volume of componenti in phasej, respectively, and are composition independent. Two graphical evaluation methods for obtaining the interdiffusion coefficients for all the phases present in the diffusion zone have been developed in infinite and semi-infinite media. Concentration-distance curves of both the components for an infinite medium and those curves and also mass change of the couple per unit area of the surface before and after the diffusion anneal for a semi-infinite medium must be prepared to calculate an interdiffusion coefficient for each phase.     

Interaction of deformation twin and 120 deg-rotational order fault domain boundary in the lamellar structure of two-phase TiAl-based alloys

Interactions between deformation twin and 120 deg-rotational domain boundary were studied by transmission electron microscopy in a two-phase TiAl-based alloy with fully lamellar structure deformed at room temperature. Three types of the interaction were observed, depending on the interaction geometry and crystallography faced by the incident twinning Shockleys. It was found that the incident twinning shear could be accommodated into the barrier domain by a reaction involving emission of 1/2 {111} _B slip in all the three types of interactions presumably since the slip required a small critical resolved shear stress (CRSS) and was always favored by the pile-up stress. Several reaction schemes involving 1/2 {111} _B slip for each type of the interactions were proposed by considering whether the reaction resulted in a reduced elastic energy and if the dissociated dislocations were able to glide away to minimize the total elastic energy associated with a long-range stress field of a pileup of the incident twinning partials. It is suggested that whether a reaction scheme is feasible would depend on behavior of other product dislocation except 1/2 {111} _B .     

Interdiffusion in Ni-rich,Ni-Cr-Al alloys at 1100 and 1200 °C: Part II. Diffusion coefficients and predicted concentration profiles

Ternary interdiffusion coefficients were measured in the Ni solid solution γ (fcc) phase of the Ni-Cr-Al system at 1100 and 1200 °C. Extensive use was made of both γ/γ and γ/γ + β (β-NiAl structure) diffusion couples. Two analysis techniques were employed to calculate the interdiffusion coefficients. When the Matano planes for Al and Cr were not coincident, numerous integral calculations were made to determine an average diffusion coefficient and to assess the effect of the noncoincidence of the Matano planes. The results of the diffusivity measurements showed that is approximately four times greater than , while and are of the same magnitude. For all concentrations, is two to three times greater than . Both and increase with increasing Al concentration, whereas and show little concentration dependence on Cr alone. A ternary, finite-difference interdiffusion model was employed to predict concentration profiles for the γ/γ couples utilizing the concentration dependence of the measured diffusivities. Good agreement was observed between the predicted and measured concentration profiles for both 1100 and 1200 °C.     

Effect of solidification cooling rate on the morphology and number per unit volume of primary Mg<Subscript>2</Subscript>Si particles in a hypereutectic Al-Mg-Si alloy

Growth morphology and number per unit volume have been determined vs withdrawal velocity V over the range 0.1 to 4 mm/s for primary Mg₂Si in a Bridgman-solidified hypereutectic Al-Mg-Si alloy. Primary Mg₂Si shows a transition from irregular or regular polyhedral to dendritic with increasing V, and increases with solidification cooling rate according to the relationship . These results are compared with corresponding ones for Al-Mg-Si alloy wedge castings and for primary silicon in hypereutectic Al-Si alloys.     

The development of the deformation texture in zirconium during rolling in sequential passes

Slip and twinning systems activated by rolling in sequential passes were observed on a coarse grained zirconium polycrystal. At least five independent deformation modes are activated; slip and twinning systems occur simultaneously. For low degrees of deforma-tion the main slip system is prism slip , even when the orientation is not favorable. The lattice rotations caused by slip proceed gradually with increasing defor-mation; they are relatively small although the strain achieved can be large. On the other hand, twinning causes spontaneous, large-scale lattice rotations, even for low degrees of deformation. The type of twinning depends largely on the crystallographic orientation of the matrix. For basal pole orientations of the undeformed grains in the area 0 to 50 deg from the normal direction twinning becomes preferentially operative. For basal pole orientations of the undeformed grains in the area 50 to 90 deg from the normal direction, however, twinning becomes preferentially operative. In both orientation areas as a complementary system twinning is operative. For all deformation sys-tems their operation is independent of the azimutal position of the basal pole in these areas. The lattice rotations alter the orientation of the crystallites in such a way that the basal poles all become aligned more or less in the direction of the deforming compres-sive force. For higher degrees of deformation pyramidal slip with a (c + a) type Burgers Vector can explain why this preferred orientation is maintained as final position, which for zirconium shows a split of basal poles of ±30 to 50 deg towards the transverse direc-tion. The method of following the complicated interactions between different slip and twinning systems in a stepwise deformed, coarse grained sheet by 1) trace analysis of the deformation modes, 2) by correspondingly derived lattice rotations, and 3) by texture measurements leads to an explanation of the texture development in zirconium. It is dis-cussed on the basis of basal pole rotations.     

An electron-backscattered diffraction study of the texture evolution in a coarse-grained AZ31 magnesium alloy deformed in tension at elevated temperatures

Electron-backscattered diffraction (EBSD) has been used to investigate the texture evolution during tensile deformation at temperatures between 673 and 773 K of a coarse-grained commercial AZ31 magnesium alloy. A weak (0001) fiber texture was initially present in the hot-rolled magnesium alloy plate. The [0001] directions of the grains spread 0 to 45 deg around the normal direction (ND) of the magnesium alloy plate. This pre-existing weak texture evolved during tensile deformation into a strong texture close to the {0001} 〈1 00〉. The [0001] directions of the grains rotated toward the orientations perpendicular to the tension axis of the samples, indicating that the 〈11 0〉 slip system appeared to be the most active slip system, especially in the early stages of deformation. The EBSD Schmid-factor analysis revealed that, however, with an increase in strain and the rotation of the (0001) slip plane, the {11 2} 〈11 〉 slip system appeared to be more favorable. The {1 00} 〈11 0〉 and {1 01} 〈11 0〉 slip systems remained favored throughout the strains investigated, indicating that {1 00} and {1 01} are two important slip planes for cross slip using the 〈11 0〉 slip vector. It is found that the misorientation across one coarse grain (as high as 38.2 deg) is accommodated by low-angle grain boundaries (LAGBs). The formation of these LAGBs may be an intermediate stage of the coarse grain refinement that occurred during deformation. This article is based on a presentation made in the symposium entitled “Processing and Properties of Structural Materials,” which occurred during the Fall TMS meeting in Chicago, Illinois, November 9–12, 2003, under the auspices of the Structural Materials Committee.     

Coarsening of dispersed intermetallic

Dendritic monocrystals of Al-4.5 wt pct Cu-2 wt pct Mn were directionally solidified at 0.20 m/h under a thermal gradient of 3 × 10³ K/m. Crystal pulling was stopped for various lengths of time prior to quenching the remaining liquid, thus making it possible to evaluate the transformation and coarsening kinetics of dispersed intermetallic phases, Al₆Mn and Al₂₀Cu₂Mn₃, as a function of temperature. Coarsening of Al₆Mn intermetallic particles surrounded by liquid (Type II) follows an average particle size relationship much closer than it does a relationship. This suggests that convection plays no important role in coarsening. For coarsening of Al₆Mn particles in a solid matrix (Type I) the relationship fits the experimental measurements reasonably well. Coarsening kinetics studies were extended to intermetallic particle sizes an order of magnitude finer than those occurring in directionally solidified alloy, in order to derive information required by an on-going project on the effect of intermetallic phase geometry on corrosion behavior. Jt was found that coarsening of Al₂₀Cu₂Mn₃ particles contained in a melt-spun ribbon follows a relationship, as predicted by Kirchner for grain-boundary diffusion-controlled ripening. Finally, coarsening of Al₆Mn particles surrounded by liquid indium film and contained in a plastically deformed matrix follows a relationship, as predicted by LSW theory for liquid diffusion-controlled ripening. Shortening the time required to obtain coarse intermetallic particles during a homogenization treatment is important in deep drawing. Formerly Graduate Student, Department of Metallurgy, University of Connecticut, Storrs, CT 06268     

Martensitic transformation in Zr−Ti alloys

Martensitic transformation in a series of Zr−Ti alloys has been studied by transmission electron microscopy. A transition in morphology and substructure was observed with increasing additions of titanium. The 5 wt pct Ti alloy was found to be predominantly dislocated lath martensite while the 10 wt pct Ti alloy showed mainly a twinned plate morphology. Twins within the martensite plates could be classified into two categories, namely, thick twins and thin twins mainly on planes and, to a lesser extent, on and planes. In the case of the thick twins, the specific variant of the twin plane was always found to correspond to a plane of the {110}_bcc type, which is a mirror plane in the parent bcc crystal. When the specific variant of the composition plane was not parallel to a mirror plane, the twins were observed to be very thin. Evidence of slip within individual twin bands pointed to the operation of a multiple shear inhomogeneous deformation. Observations concerning deformation twins due to impingement effect are also discussed in this paper.     

Elastic interaction stresses: Part II. The influence of orientation on stresses generated in iso-axial bicrystals

The effects of four types of incompability on stresses generated in seven iso-axial bicrystals of 70-30 alpha brass subjected to tension were examined by finite element methods. The distribution of applied stress and resolved shear stresses was determined. The applied stress, { }, was higher at the interior than at the surface, while the resolved shear stresses were generally higher at the surface. For both applied { } and resolved shear stresses, the largest stresses occurred at the bicrystal boundaries. The effect of end constraints on a [213] oriented single crystal was found to create nonuniform stresses and strains, and an explanation for this behavior was proposed. The effect of orientation on the magnitude of grain boundary resolved shear stress, { }, and the relative extent (volume fraction) of enhanced grain boundary resolved shear stress,V _gb, were determined. The highest values of { } andV _gb were reached in different portions of the stereographic triangle. The elastic interactions producing this behavior were too complex to permit a simple interpretation. TZI-KANG CHEN formerly Graduate Student at Polytechnic University     

Deformation of a Burgers oriented bimetallic bicrystal of alpha-beta (Ti-13Mn)

The deformation behavior of a Burgers oriented α-β-Ti-13Mn bimetallic bicrystal was studied at two plastic strains, 0.52 and 2.08 pct. Two single crystals, α and β, each corresponding to the orientation of its respective bicrystal component were also investigated. The stress axes were and [1218]_β. The interface planes were and and lay in the x’-z’ plane. The deformation behavior of the a component differed from that of the a single crystal because of plastically induced stresses,T _y’z’ ,T _x’z’ ,T _x’y’ , and σ _x’x’ . Prismatic slip and twinning were found in the single crystal α whereas the bicrystal revealed additionally pyramidal andc + a slip, the latter at the interface. Slip on the front and back surfaces was different and both thec + a and twinning systems acted to maintain compatibility. Slip in the β single crystal and the β bicrystal component were quite similar. However, there were differences in the intensity and amount of primary slip, (231) , on the front and back surfaces. The diminished amount of (231) slip on the back surface was due to plastically induced stresses, and on the front surface the primary slip cross slipped to slip which triggeredc + a slip in α. On the back surface the dominant slip system was which acted in response to the plastically induced stresses. An approximate calculation revealed that the interface deformation zone had about twice the flow stress of the average bicrystal stress. Formerly a Graduate Student in the Department of Physical and Engineering Metallurgy at Polytechnic Institute of New York, Brooklyn, NY     

Deformation twinning and texture variation in Zr-2.5 pct Nb alloy during rolling

Recently, it was proven that delayed hydride cracking (DHC) is accompanied by deformation twinning through the texture analysis of a fractured surface. Thus, in order to understand the operation of deformation twinning, the texture variations by rolling were investigated using Zr-2.5 pct Nb alloy with {11 0} 〈10 0〉 texture. It was observed that deformation twinning was operated predominantly in the range of a 5 to 15 pct strain. The basal poles were rotated in the normal direction of a rolling plane with the strain, and the (0002) texture was fully reversed after 15 pct strain. This finding was established to be due to the operation of the {10 2} and {11 1} twinning systems through the analysis of the inverse pole figure. It appeared that the degree and easiness of the twinning operation was affected by changing the direction of compression during rolling with respect to the initial {11 0} 〈10 0〉 texture. The contribution of deformation twinning to strain was quantitatively calculated using the change in the basal pole components. This article is based on a presentation made in the symposium entitled “Processing and Properties of Structural Materials,” which occurred during the Fall TMS meeting in Chicago, Illinois, November 9–12, 2003, under the auspices of the Structural Materials Committee.     

Molecular Dynamics simulation of 〈 c + a 〉 dislocation core structure in hexagonal-close-packed metals

The core structures of 〈c+a〉 dislocations in hexagonal-close-packed (hcp) metals have been investigated by molecular dynamics (MD) simulation using a Lennard-Jones-type pair potential. The 〈c+a〉 edge dislocation has two types of core at 0 K; one is a perfect dislocation (type A), and the other has two 1/2 〈c+a〉 partials (type B). Type A transforms to type B by abruptly increasing temperature from 0 K to 293 K, while type B is stable in temperature range from 0 K to 293 K. In contrast, type A extends parallel to (0001) at 30 K, and this extended core is still stable at 293 K. These results suggest that the 〈c+a〉 edge dislocation glides on the as two 1/2 〈c+a〉 partial dislocations and becomes sessile, due to changes of the core structure. The 〈c+a〉 screw dislocation spreads over two planes at 0 K. The core transforms into a unsymmetrical structure at 293 K, which is spread over and , and core spreading occurs parallel to at 1000 K. A critical strain to move screw dislocations depends on the sense of shear strain. The dependence of the yield stress on the shear direction can be explained in terms of these core structures. This article is based on a presentation made in the symposium entitled “Dect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Interface migration during recrystallization: The role of recovery and stored energy gradients

The interface migration rate behavior during recrystallization of a deformed iron single crystal is considered in detail. A spheroidal growth, site-saturated nucleation model of recrystallization is developed for iron which quantitatively takes into account the effect of concurrent recovery in the deformed regions ahead of the advancing recrystallization interfaces. The recovery kinetics model incorporated into the growth model was devised based on the experimental data of Michalak and Paxton.[10] Explanations are advanced for the nonlinear growth of grains during recrystallization of iron. Deformation-induced stored energy gradients are proposed to explain the aspects of nonlinear growth not accounted for by recovery and are introduced into the growth model also. A localized shear band deformation mechanism developed by Harataniet al.[14] is used to rationalize the presence of stored energy gradients in the deformed iron single crystal.     

Influence of secondary precipitates and crystallographic orientation on the strength of single crystals of a Ni-based superalloy

The effect of crystallographic orientation and aging heat treatment at 850 °C on the creep rupture strength of single crystals of a nickel-based superalloy was examined at 700 °C in detail. Initial tensile orientations were selected over a wide range on the standard stereographic triangle. The {111}〈112〉-type slip systems were found to be operative during the creep deformation. The creep behavior was found to be greatly influenced by the additional aging at 850 °C for 20 hours. It was found that the effect of the aging at 850 °C was quite different between orientations favored for the slip system and those favored for the (111) slip system and that the creep deformation mechanisms of these two slip systems were different. In the orientations favored for slip systems, in the single-aged specimens, a small mean surface-to-surface spacing due to hyperfine γ′ precipitates in the matrix channel promoted the slip and the primary creep. As a result of the additional aging at 850 °C, the hyperfine γ′ precipitates were dissolved into the matrix, and the resultant large mean surface-to-surface spacing between the cuboidal precipitates inhibited extensive shearing of the γ-γ′ structure by the slip system. As a result, the creep strengths of these orientations were increased in double-aged specimens; however, the low ductility associated with the difficulty of secondary noncoplanar slip did not enlarge rupture lifetime in the double-aged [001] specimen. In the orientations favored for the (111) slip system, creep deformation occurred by twinning shear through γ and γ′ precipitates, and a distinct effect of the aging at 850 °C was not observed. In the multiple orientation of the {111} -type slip systems, i.e., the and orientations, hyperfine precipitates improved creep strength because they prevented dislocations from gliding in the matrix channel in the single-aged specimens.     

Microstructural modeling of recrystallization in deformed iron single crystals

Recrystallization kinetics in a (111)[1 0] iron single crystal deformed 70 pet by rolling were characterized experimentally at temperatures between 500°C and 600°C by means of quantitative metallography. A Laplace transform method was applied to the time-dependent global microstructural properties, volume fraction, interface area per unit volume, and the largest intercept-free length (recrystallized grain) to separate nucleation and interface migration effects from the overall recrystallization kinetics. A comprehensive nucleation and growth model was derived from analysis of the microstructural data. The model consisted of the following salient features: (a) nucleation was random and approximately site-saturated with zero incubation time at all temperatures; (b) the recrystallized grains grew three-dimensionally in the shape of prolate spheroids; and (c) interface migration rates were highly anisotropic, the grains growing at an approximately constant rate in one dimension and at a strongly decreasing rate in the other two dimensions. The present findings were compared to a similar earlier study of a deformed iron (111)[ 2] single crystal. The time dependencies of the interface migration rates were rationalized in terms of a deformation-induced, nonuniform distribution of stored energy and an orientation-dependent grain boundary mobility.     

Interdiffusion in ternary Fe-Cr-AI alloys

Interdiffusion coefficient matrices, have been experimentally measured at 31 points in the αδFe phase field of the Fe-Cr-AI ternary equilibrium phase diagram at 900 °C (1173 K). Analyses of the computed matrices were carried out by subjecting each measured -Dⁿ _ij to two consistency tests comprised of Onsager’s and Kirkaldy’s relations. Good consistency with these relationships was obtained in the central region of the ternary phase field, but there were significant deviations near the phase boundaries. These may beattributable to systematic uncertainties in the analytical procedure. The results indicate that falls quickly with increasing C_Cr, with C_Al > 0.2, but is not a strong function of C_Al. Conversely, is not a strong function of C_Al but decreases with increasing C_Cr. formerly with the Lawrence Berkeley Laboratories of the University of California, Berkeley At the time of this research, Dr. Stringer was on sabbatical leave at the Lawrence Berkeley Laboratories, Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720.