Geometrical properties of the vorticity vector derived using large-eddy simulation

In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor and negative subgrid-scale stress tensor -τ_ij, enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of , and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of -τ_ij is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of -τ_ij and are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of .     

Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension

The membrane deflection experiment developed by Espinosa and co-workers was used to examine size effects on mechanical properties of free-standing polycrystalline FCC thin films. We present stress-strain curves obtained on films 0.2, 0.3, 0.5 and thick including specimen widths of 2.5, 5.0, 10.0 and for each thickness. Elastic modulus was consistently measured in the range of 53- for Au, 125- for Cu and 65- for Al. Several size effects were observed including yield stress variations with membrane width and film thickness in pure tension. The yield stress of the membranes was found to increase as membrane width and thickness decreased. It was also observed that thickness plays a major role in deformation behavior and fracture of polycrystalline FCC metals. A strengthening size scale of one over film thickness was identified. In the case of Au free-standing films, a major transition in the material inelastic response occurs when thickness is changed from 1 to . In this transition, the yield stress more than doubled when film thickness was decreased, with the thick specimen exhibiting a more brittle-like failure and the thick specimen exhibiting a strain softening behavior. Similar plasticity size effects were observed in Cu and Al. Scanning electron microscopy performed on Au films revealed that the number of grains through the thickness essentially halved, from approximately 5 to 2, as thickness decreased. It is postulated that this feature affects the number of dislocations sources, active slip systems, and dislocation motion paths leading to the observed strengthening. This statistical effect is corroborated by the stress-strain data in the sense that data scatter increases with increase in thickness, i.e., plasticity activity.The size effects here reported are the first of their kind in the sense that the measurements were performed on free-standing polycrystalline FCC thin films subjected to macroscopic homogeneous axial deformation, i.e., in the absence of deformation gradients, in contrast to nanoindentation, beam deflection, and torsion, where deformation gradients occur. To the best of our understanding, continuum plasticity models in their current form cannot capture the observed size scale effects.     

Discrete dislocation plasticity analysis of the wedge indentation of films

The plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at ±35.3^° and 90^° with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2, 10 and , and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths . On the other hand, for the films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and thick films sink-in occurs around the indenter, while pile-up occurs in the film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact size-independent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 43, 411-423]; and (iii) the computed contact area is compared with that obtained from the estimation procedure of Oliver and Pharr [1992. An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7, 1564-1583].     

Deformation of FCC nanowires by twinning and slip

We present atomistic simulations of the tensile and compressive loading of single crystal face-centered cubic (FCC) nanowires with and orientations to study the propensity of the nanowires to deform via twinning or slip. By studying the deformation characteristics of three FCC materials with disparate stacking fault energies (gold, copper and nickel), we find that the deformation mechanisms in the nanowires are a function of the intrinsic material properties, applied stress state, axial crystallographic orientation and exposed transverse surfaces. The key finding of this work is the first order effect that side surface orientation has on the operant mode of inelastic deformation in both and nanowires. Comparisons to expected deformation modes, as calculated using crystallographic Schmid factors for tension and compression, are provided to illustrate how transverse surface orientations can directly alter the deformation mechanisms in materials with nanometer scale dimensions.     

Glass-modified stress waves for adhesion measurement of ultra thin films for device applications

Laser-generated stress wave profiles with rarefaction shocks (almost zero post-peak decay times) have been uncovered in different types of glasses and presented in this communication. The rise time of the pulses was found to increase with their amplitude, with values reaching as high as . This is in contrast to measurements in other brittle crystalline solids where pulses with rise times of and post-peak decay times of were recorded. The formation of rarefaction shock is attributed to the increased compressibility of glasses with increasing pressures. This was demonstrated using a one-dimensional nonlinear elastic wave propagation model in which the wave speed was taken as a function of particle velocity. The technological importance of these pulses in measuring the tensile strength of very thin film interfaces is demonstrated by using a previously developed laser spallation experiment in which a laser-generated compressive stress pulse in the substrate reflects into a tensile wave from the free surface of the film and pries off its interface at a threshold amplitude. Because of the rarefaction shock, glass-modified waves allow generation of substantially higher interfacial tensile stress amplitudes compared with those with finite post-peak decay profiles. Thus, for the first time, tensile strengths of very strong and ultra thin film interfaces can be measured. Results presented here indicate that interfaces of 185-nm-thick films, and with strengths as high as , can be measured. Thus, an important advance has been made that should allow material optimization of ultra thin layer systems that may form the basis of future MEMS-based microelectronic, mechanical and clinical devices.     

A perturbation-incremental method for strongly non-linear non-autonomous oscillators

A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form , where g(x) and are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed.     

Superhard silicon nanospheres

Successful deposition and mechanical probing of nearly spherical, defect-free silicon nanospheres has been accomplished. The results show silicon at this length scale to be up to four times harder than bulk silicon. Detailed measurements of plasticity evolution and the corresponding hardening response in normally brittle silicon is possible in these small volumes. Based upon a proposed length scale related to the size of nanospheres in the 20- radii range, a prediction of observed hardnesses in the range of 20- is made. The ramifications of this to computational materials science studies on identical volumes are discussed.     

Large electrostrictive actuation of barium titanate single crystals

An experimental investigation of the electromechanical behavior of single crystals of the ferroelectric perovskite barium titanate is presented. An experimental setup has been designed to investigate large strain actuation in single crystal ferroelectrics subjected to combined electrical and mechanical loading. Experiments have been performed on initially single domain crystals of barium titanate with (100) and (001) orientation at compressive stresses between 0 and . Global strain and polarization histories have been recorded. The electrostrictive response is shown to be highly dependent on the level of applied stress with a maximum strain of 0.9% measured at a compressive stress of about and electric field of about . This level of strain is about 5 times higher than in typical commercial piezoelectric PZT. Polarized light microscopy has been used to observe the evolution of the domain pattern simultaneously with the strain and polarization measurement. The observations reveal that the observed large strain behavior is the result of 90° domain switching.