Prevalence Of Shear Banding In Compression Of Zr41Ti14Cu12.5Ni10Be22.5 Pillars As Small As 150 Nm In Diameter

Recently, the size dependence of mechanical behaviors, particularly the yield strength and plastic deformation mode, of bulk metallic glasses (BMG) has created a great deal of interest. Contradicting conclusions have been drawn by different research groups, based on various experiments on different BMG systems. Based on in situ compression transmission electron microscopy (TEM) experiments on Zr41Ti14Cu12.5Ni10Be22.5 (Vit 1) nanopillars, this paper provides strong evidence that shear banding still prevails at specimen length scales as small as 150 nm in diameter. This is supported by in situ and ex situ images of shear bands, and by the carefully recorded displacement bursts under load control its well as load drops under displacement control. Finite element modeling of the stress state within the pillar shows that the unavoidable geometry constraints accompanying such experiments impart a strong effect on the experimental results, including non-uniform stress distributions and high level hydrostatic pressures. The seemingly improved compressive ductility is believed to be due to such geometry constraints. Observations underscore the notion that the mechanical behavior of metallic glasses, including strength and plastic deformation mode, is size independent at least in Vit 1. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Prediction Of Shear-Band Thickness In Metallic Glasses

We derive an explicit expression for predicting the thicknesses of shear bands in metallic glasses. The model demonstrates that the shear-band thickness is mainly dominated by the activation size of the shear transformation zone (STZ) and its activation free volume concentration. The predicted thicknesses agree well with the results of measurements and simulations. The underlying physics is attributed to the local topological instability of the activated STZ. The result is of significance in understanding the origin of inhomogeneous flow in metallic glasses. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Inherent Shear-Dilatation Coexistence In Metallic Glass

Shear deformation can induce normal stress or hydrostatic stress in metallic glasses [ Nature Mater. 2 ( 2003) 449, Intermetallics 14 ( 2006) 1033]. We perform the bulk deformation of three-dimensional Cu46Zr54 metallic glass (MG) and Cu single crystal model systems using molecular dynamics simulation. The results indicate that hydrostatic stress can incur shear stress in MG, but not in crystal. The resultant pronounced asymmetry between tension and compression originates from this inherent shear-dilatation coexistence in MG.

Characterization Of Shear Bands In Two Bulk Metallic Glasses With Different Inherent Plasticity

Shear banding characterization of Zr64.13Cu15.75Ni10.12Al10 and Zr65Cu15Ni10Al10 bulk metallic glasses (BMGs) with significant difference in inherent plasticity and quite similar chemical composition was studied by depth sensitive macroindentaion tests with conical indenter. Well-developed shear band pattern can be found for both BMGs after indentation. Distinct difference in the shear band spacing, scale of plastic deformation region and the shear band branching in the two BMGs account for the different plasticity.

On the origin of shear banding instability in metallic glasses

To uncover the physical origin of shear-banding instability in metallic glass (MG), a theoretical description of thermo-mechanical deformation of MG undergoing one-dimensional simple shearing is presented. The coupled thermo-mechanical model takes into account the momentum balance, the energy balance and the dynamics of free volume. The interplay between free-volume production and temperature increase being two potential causes for shear-banding instability is examined on the basis of the homogeneous solution. It is found that the free-volume production facilitates the sudden increase in the temperature before instability and vice versa. A rigorous linear perturbation analysis is used to examine the inhomogeneous deformation, during which the onset criteria and the internal length and time scales for three types of instabilities, namely free-volume softening, thermal softening and coupling softening, are clearly revealed. The shear-banding instability originating from sole free-volume softening takes place easier and faster than that due to sole thermal softening, and dominates in the coupling softening. Furthermore, the coupled thermo-mechanical shear-band analysis does show that an initial slight distribution of local free volume can incur significant strain localization, producing a shear band. During such a localization process, the local free-volume creation occurs indeed prior to the increase in local temperature, indicating that the former is the cause of shear localization, whereas the latter is its consequence. Finally, extension of the above model to include the shear-induced dilatation shows that such dilatation facilitates the shear instability in metallic glasses.

Space-time correlations of fluctuating velocities in turbulent shear flows

Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation DNS of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shearinduced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the spacetime correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

Geological evolution of two crustal scale shear zones. Part I. The Rand thrust complex, northwestern Mojave Desert, California. Part II. The Magdalena metamorphic core complex, north central Sonora, Mexico

The geology and structure of two crustal scale shear zones were studied to understand the partitioning of strain within intracontinental orogenic belts. Movement histories and regional tectonic implications are deduced from observational data. The two widely separated study areas bear the imprint of intense Late Mesozoic through Middle Cenozoic tectonic activity. A regional transition from Late Cretaceous-Early Tertiary plutonism, metamorphism, and shortening strain to Middle Tertiary extension and magmatism is preserved in each area, with contrasting environments and mechanisms. Compressional phases of this tectonic history are better displayed in the Rand Mountains, whereas younger extensional structures dominate rock fabrics in the Magdalena area.

In the northwestern Mojave desert, the Rand Thrust Complex reveals a stack of four distinctive tectonic plates offset along the Garlock Fault. The lowermost plate, Rand Schist, is composed of greenschist facies metagraywacke, metachert, and metabasalt. Rand Schist is structurally overlain by Johannesburg Gneiss (= garnet-amphibolite grade orthogneisses, marbles and quartzites), which in turn is overlain by a Late Cretaceous hornblende-biotite granodiorite. Biotite granite forms the fourth and highest plate. Initial assembly of the tectonic stack involved a Late Cretaceous? south or southwest vergent overthrusting event in which Johannesburg Gneiss was imbricated and attenuated between Rand Schist and hornblende-biotite granodiorite. Thrusting postdated metamorphism and deformation of the lower two plates in separate environments. A post-kinematic stock, the Late Cretaceous Randsburg Granodiorite, intrudes deep levels of the complex and contains xenoliths of both Rand Schist and mylonitized Johannesburg? gneiss. Minimum shortening implied by the map patterns is 20 kilometers.

Some low angle faults of the Rand Thrust Complex formed or were reactivated between Late Cretaceous and Early Miocene time. South-southwest directed mylonites derived from Johannesburg Gneiss are commonly overprinted by less penetrative north-northeast vergent structures. Available kinematic information at shallower structural levels indicates that late disturbance(s) culminated in northward transport of the uppermost plate. Persistence of brittle fabrics along certain structural horizons suggests a possible association of late movement(s) with regionally known detachment faults. The four plates were juxtaposed and significant intraplate movements had ceased prior to Early Miocene emplacement of rhyolite porphyry dikes.

In the Magdalena region of north central Sonora, components of a pre-Middle Cretaceous stratigraphy are used as strain markers in tracking the evolution of a long lived orogenic belt. Important elements of the tectonic history include: (1) Compression during the Late Cretaceous and Early Tertiary, accompanied by plutonism, metamorphism, and ductile strain at depth, and thrust driven? syntectonic sedimentation at the surface. (2) Middle Tertiary transition to crustal extension, initially recorded by intrusion of leucogranites, inflation of the previously shortened middle and upper crustal section, and surface volcanism. (3) Gravity induced development of a normal sense ductile shear zone at mid crustal levels, with eventual detachment and southwestward displacement of the upper crustal stratigraphy by Early Miocene time.

Elucidation of the metamorphic core complex evolution just described was facilitated by fortuitous preservation of a unique assemblage of rocks and structures. The "type" stratigraphy utilized for regional correlation and strain analysis includes a Jurassic volcanic arc assemblage overlain by an Upper Jurassic-Lower Cretaceous quartz pebble conglomerate, in turn overlain by marine strata with fossiliferous Aptian-Albian limestones. The Jurassic strata, comprised of (a) rhyolite porphyries interstratified with quartz arenites, (b) rhyolite cobble conglomerate, and (c) intrusive granite porphyries, are known to rest on Precambrian basement north and east of the study area. The quartz pebble conglomerate is correlated with the Glance Conglomerate of southeastern Arizona and northeastern Sonora. The marine sequence represents part of an isolated arm? of the Bisbee Basin.

Crosscutting structural relationships between the pre-Middle Cretaceous supracrustal section, younger plutons, and deformational fabrics allow the tectonic sequence to be determined. Earliest phases of a Late Cretaceous-Early Tertiary orogeny are marked by emplacement of the 78 ± 3 Ma Guacomea Granodiorite (U/Pb zircon, Anderson et al., 1980) as a sill into deep levels of the layered Jurassic series. Subsequent regional metamorphism and ductile strain is recorded by a penetrative schistosity and lineation, and east-west trending folds. These fabrics are intruded by post-kinematic Early Tertiary? two mica granites. At shallower crustal levels, the orogeny is represented by north directed thrust faulting, formation of a large intermontane basin, and development of a pronounced unconformity. A second important phase of ductile strain followed Middle Tertiary? emplacement of leucogranites as sills and northwest trending dikes into intermediate levels of the deformed section (surficial volcanism was also active during this transitional period to regional extension). Gravitational instabilities resulting from crustal swelling via intrusion and thermal expansion led to development of a ductile shear zone within the stratigraphic horizon occupied by a laterally extensive leucogranite sill. With continued extension, upper crustal brittle normal faults (detachment faults) enhanced the uplift and tectonic denudation of this mylonite zone, ultimately resulting in southwestward displacement of the upper crustal stratigraphy.

Strains associated with the two ductile deformation events have been successfully partitioned through a multifaceted analysis. R_f/Ø measurements on various markers from the "type" stratigraphy allow a gradient representing cumulative strain since Middle Cretaceous time to be determined. From this gradient, noncoaxial strains accrued since emplacement of the leucogranites may be removed. Irrotational components of the postleucogranite strain are measured from quartz grain shapes in deformed granites; rotational components (shear strains) are determined from S-C fabrics and from restoration of rotated dike and vein networks. Structural observations and strain data are compatable with a deformation path of: (1) coaxial strain (pure shear?), followed by (2) injection of leucogranites as dikes (perpendicular to the minimum principle stress) and sills (parallel to the minimum principle stress), then (3) southwest directed simple shear. Modeling the late strain gradient as a simple shear zone permits a minimum displacement of 10 kilometers on the Magdalena mylonite zone/detachment fault system. Removal of the Middle Tertiary noncoaxial strains yields a residual (or pre-existing) strain gradient representative of the Late Cretaceous-Early Tertiary deformation. Several partially destrained cross sections, restored to the time of leucogranite emplacement, illustrate the idea that the upper plate of the core complex bas been detached from a region of significant topographic relief. 50% to 100% bulk extension across a 50 kilometer wide corridor is demonstrated.

Late Cenozoic tectonics of the Magdalena region are dominated by Basin and Range style faulting. Northeast and north-northwest trending high angle normal faults have interacted to extend the crust in an east-west direction. Net extension for this period is minor (10% to 15%) in comparison to the Middle Tertiary detachment related extensional episode.