A correspondence principle for fractal and classical cracks

In this paper we introduce a correspondence principle between fractal cracks and notches. This correspondence principle defines an equivalent smooth blunt crack for a fractal crack. Once this transformation is accomplished, the laws of linear elastic fracture mechanics apply. Since the root radius of the equivalent crack is finite, the crack may be further reduced to a notch visualized as an elongated elliptical void. Therefore, the laws of the LEFM and those of Neuber’s ‘notch mechanics’ coincide, and they can be used interchangeably. In other words, we have shown that the three mathematical representations of discontinuities in the displacement field, a notch, a classic Griffith crack and a fractal crack, are related, and the pertinent relationships are determined by the proposed correspondence principle. We also give an estimation of the size of the plastic region ahead of a self-similar (or self-affine) fractal crack tip.     

Computational Modeling of Microstructural-Evolution in AISI 1005 Steel During Gas Metal Arc Butt Welding

A fully coupled (two-way), transient, thermal-mechanical finite-element procedure is developed to model conventional gas metal arc welding (GMAW) butt-joining process. Two-way thermal-mechanical coupling is achieved by making the mechanical material model of the workpiece and the weld temperature-dependent and by allowing the potential work of plastic deformation resulting from large thermal gradients to be dissipated in the form of heat. To account for the heat losses from the weld into the surroundings, heat transfer effects associated with natural convection and radiation to the environment and thermal-heat conduction to the adjacent workpiece material are considered. The procedure is next combined with the basic physical-metallurgy concepts and principles and applied to a prototypical (plain) low-carbon steel (AISI 1005) to predict the distribution of various crystalline phases within the as-welded material microstructure in different fusion zone and heat-affected zone locations, under given GMAW-process parameters. The results obtained are compared with available open-literature experimental data to provide validation/verification for the proposed GMAW modeling effort.     

Nonlocal effect on the diamagnetic susceptibility of a granular superconductor

The diamagnetic susceptibility of the granular superconductors in the presence of dilute impurity concentration including non-local electron scattering in the clean superconductor in the limit of strong magnetic fields and low temperatures is calculated. I will show that diamagnetic susceptibility goes to a constant value independent of magnetic field due to non-local effect, while in the local limit it diverges in a power law near the critical field.     

On applications of generalized functions to the analysis of Euler–Bernoulli beam–columns with jump discontinuities

In this article some applications of the distribution theory of Schwarz to the analysis of beam–columns with various jump discontinuities are offered. The governing differential equation of an Euler–Bernoulli beam–column with jump discontinuities in flexural stiffness, displacement, and rotation, and under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam–column method is introduced. Using this method, instead of solving the differential equation of the beam–column in the space of generalized functions, another differential equation can be solved in the space of classical functions. Some examples of beam–columns and columns with various jump discontinuities are solved. Deflections of beam–columns and buckling loads for columns with jump discontinuities are calculated using the Laplace transform method in the space of generalized functions.     

A hybrid CT/DT double-sampled SMASH Σ? modulator for broadband applications in 90?nm CMOS technology

In this paper, a hybrid continuous-time (CT)/discrete-time (DT) multi-stage noise shaping (MASH) sigma?Cdelta (????) modulator architecture for broadband applications is presented. The double-sampling technique is employed in the DT second-stage modulator in order to reduce the power consumption of the overall modulator. Flat and unity signal transfer functions are used in the first- and second-stage modulators, respectively, to relax the output swing of the analog building blocks without influencing the inherent anti-aliasing behavior of the first-stage CT modulator. The proposed structure is insensitive to the amplifier limited dc gain of CT stage and avoids the need of compensation for finite gain-bandwidth induced error in CT loop filter. As a design example, the proposed MASH 2-2 modulator is designed in a 90?nm CMOS technology with 1?V power supply. Circuit level simulation results with HSPICE achieve the maximum SNDR of 74.8?dB and dynamic range of 76.5?dB in 12.5?MHz bandwidth with 17?mW power consumption while operating at 200?MHz sampling rate.     

Synergy derived by combining graphene and carbon nanotubes as nanofillers in composites

Both one-dimensional carbon nanotubes as well as two-dimensional graphene sheets have been extensively investigated as nanofillers in composites. However there are very few reports on their combined use in composite materials. Here we report the mechanical properties including Young's modulus, tensile strength and fatigue properties of an epoxy polymer reinforced with various combinations of graphene and carbon nanotube fillers- i.e., nanotubes alone, graphene alone and a mixture of graphene and nanotubes. We find that at low nanofillers loadings (< 0.1% weight), the graphene fillers performed better than both singlewalled as well as multiwalled carbon nanotubes. However, interestingly it was the combination of carbon nanotubes with graphene that yielded the greatest improvement in mechanical properties. Optical microscopy of thin micro-tomed slices of the composites indicated that in the presence of the nanotubes the graphene sheets appear to have aggregated into chains forming a network structure. Such long range ordering of the nanofillers is very unusual in a nanocomposite system and is likely responsible for the enhanced mechanical properties.     

An accurate analysis of slew rate for two-stage CMOS opamps

This brief presents a time-domain model for the slew rate of CMOS two-stage Miller compensated operational transconductance amplifiers. The effects of both the first- and second-stage currents are considered in this model and a simple analytical expression is given in terms of the compensation and load capacitors, output voltage change, and device sizes. HSPICE simulation results are provided to show the validity of the proposed model using a 0.25-/spl mu/m CMOS technology.     

Small-angle X-ray scattering from phase-separating amorphous metallic alloys undergoing nanocrystallization

We performed a combined small- and wide-angle X-ray scattering (SAXS/WAXS) study of nanocrystallization during annealing of binary Al₉₂Sm₈ and Al₉₁Gd₉ melt-spun glassy alloys. In course of the transformation an interference maximum develops in the SAXS region while WAXS spectra show formation of fcc-Al nanocrystals in the glassy phase. In order to determine the origin of the SAXS maximum the theoretical SAXS intensity and distance distribution function were calculated considering two structural models. The first model represented a single nanocrystal with a solute layer on its surface and the second one a phase-separated alloy with spatially correlated compositional fluctuations. The results of the calculations are compared with the experimental data. It is demonstrated that only the model representing correlated fluctuations reasonably reproduces the experimental results. We conclude that nano-scale glassy phase separation occurs in the investigated alloys and the nanocrystals form inside the Al-rich amorphous regions.