Scaling relationships in indentation of power-law creep solids using self-similar indenters

We use dimensional analysis to derive scaling relationships for self-similar indenters indenting solids that exhibit power-law creep. We identify the parameter that represents the indentation strain rate. The scaling relationships are applied to several types of indentation creep experiment with constant displacement rate, constant loading rate or constant ratio of loading rate over load. The predictions compare favourably with experimental observations reported in the literature. Finally, a connection is found between creep and 'indentation-size effect' (i.e. changing hardness with indentation depth or load).

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length xi and the roughness exponent alpha, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with alpha = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

The accuracy of Kirchhoff's approximation in describing the far field speckles produced by random self-affine fractal surfaces

Based on the rigorous formulation of integral equations for the propagations of light waves at the medium interface, we carry out the numerical solutions of the random light field scattered from self-affine fractal surface samples. The light intensities produced by the same surface samples are also calculated in Kirchhoff's approximation, and their comparisons with the corresponding rigorous results show directly the degree of the accuracy of the approximation. It is indicated that Kirchhoff's approximation is of good accuracy for random surfaces with small roughness value w and large roughness exponent alpha. For random surfaces with larger w and smaller alpha, the approximation results in considerable errors, and detailed calculations show that the inaccuracy comes from the simplification that the transmitted light field is proportional to the incident field and from the neglect of light field derivative at the interface.

Indentation of power law creep solids by self-similar indenters

For creep solids obeying the power law under tension proposed by Tabor, namely sigma = b(epsilon) over dot(m), it has been established through dimensional analysis that for self-similar indenters the load F versus indentation depth h can be expressed as F(t) = bh(2)(t)[(h) over dot(t)/h(t)](m)Pi(alpha) where the dimensionless factor Pi(alpha) depends on material parameters such as m and the indenter geometry. In this article, we show that by generalizing the Tabor power law to the general three dimensional case on the basis of isotropy, this factor can be calculated so that indentation test can be used to determine the material parameters b and m appearing in the original power law. Hence indentation test can replace tension test. This could be a distinct advantage for materials that come in the form of thin films, coatings or otherwise available only in small amounts. To facilitate application values of this constant are given in tabulated form for a range of material parameters. (C) 2010 Elsevier B.V. All rights reserved.

Fractals in fracture of bulk metallic glass

We investigate the nanoscale periodic corrugation (NPC) structures on the dynamic fracture surface of a typical tough bulk metallic glass, submitted to high-velocity plate impact and scanned by atomic force microscopy (AFM). The detrended fluctuation analysis (DFA) of the recorded AFM profiles reveals that the valley landscapes of the NPC are nearly memoryless, characterized by Hurst parameter of 0.52 and exhibiting a self-similar fractal character with the dimension of about 1.48. Our findings confirm the existence of the “quasi-cleavage” fracture underpinned by tension transformation zones (TTZs) in metallic glasses.

Fractal roughness characterization of super-ground Mn-Zn ferrite single crystals

The surface of superground Mn-Zn ferrite single crystal may be identified as a self-affine fractal in the stochastic sense. The rms roughness increased as a power of the scale from 10(2) nm to 10(6) nm with the roughness exponent alpha = 0.17 +/- 0.04, and 0.11 +/- 0.06, for grinding feed rate of 15 and 10 mu m/rev, respectively. The scaling behavior coincided with the theory prediction well used for growing self-affine surfaces in the interested region for magnetic heads performance. The rms roughnesses increased with increase in the feed rate, implying that the feed rate is a crucial grinding parameter affecting the supersmooth surface roughness in the machining process.

Fractals and Scaling in Fracture Induced by Microcrack Coalescence

A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.

Avalanche behavior and statistical properties in a microcrack coalescence process

Fracture owing to the coalescence of numerous microcracks can be described by a simple statistical model, where a coalescence event stochastically occurs as the number density of nucleated microcracks increases. Both numerical simulation and statistical analysis reveal that a microcrack coalescence process may display avalanche behavior and that the final failure is catastrophic. The cumulative distribution of coalescence events in the vicinity of critical fracture follows a power law and the fracture profile has self-affine fractal characteristic. Some macromechanical quantities may be traced back and extracted from the mesoscopic process based on the statistical analysis of coalescence events.

Simulation of Natural Gas Production in Hydrate Reservoirs

This paper simulates a one-dimensional physical model of natural gas production from hydrate dissociation in a reservoir by depressurization. According to the principles of solid hydrate decomposition in stratum and flow of natural gas in porous medium, the pressure governing equations for both gas zone and hydrate zone are set up based on the physical production model. Using the approximation reported by N. N. Verigin et al. (1980), the nonlinear governing equations are simplified and the self-similar solutions are obtained. Through calculation, for different reservoir parameters, the distribution characters of pressure are analyzed. The decline trend of natural gas production rate with time is also studied. The simulation results show that production of natural gas from a hydrate reservoir is very sensitive to several reservoir parameters, such as wellbore pressure and stratum porosity and permeability.

Formation and characterization of tin oxide aerogel derived from sol-gel process based on tetra(n-butoxy)tin(IV)

Transparent and translucent SnO2 aerogels with high specific surface area (>300m(2)/g) have been prepared by sol-gel process using tetra(n-butoxy)tin(IV) as a starting compound, and supercritical drying technique for solvent extraction. Light scattering measurements reveal that the polymeric cluster size distribution in sol system is gradually broadened during sol-gel transition. SEM images show that the aerogels are made up of the cottonlike oxide agglomerates with a large number of Pores. TEM images show that these aerogels seem to be self-similar at different magnifications. Their pore size distribution is pretty wide ranging, from mesopore to macropore especially for that of translucent aerogel. (C) 2004 Elsevier B.V. All rights reserved.

可重构装配系统开放式组织结构的研究

为了克服传统装配线的不足,在基于功能对象的产品族建模基础上,提出了主干线和装配模块相结合的可重构装配系统开放式组织结构。这种分形相似的组织结构具有能力柔性、鲁棒性、功能扩展能力等特点,并能通过模块的局部调整快速响应市场的需求。利用网络法,针对鲁棒性和增容性问题,提出了相应的重构优化算法。

地球化学场的多重分形分析与分解

Geochemical and Geophysical anomaly play an important role in mineral exploration，their spatial structure character include singularity and self－similar。The singularity of an anomaly reflects the enrichment characters of the geochemical element ,The anomaly separation by multifractal model is useful in mineral anomaly assessment。In recent years, The continuous multifractal mode of the geochemical fields was studied ,it can be separated into the simple continuous multifractal mode and the high concentration multifractal mode, and the C－A、C－D、 S－A、MSDV、W－A method to decompose the anomaly were presented。Those are succeeded in interpretation of Geochemical and Geophysical anomaly。 This study makes a summarization to these method， we present a multifractal method based on wavelet transform to analyze the multifractal fields 。The singularity and spectrum are calculated through tracing the wavelet maximum modulus in different measure，and then the fields can be decomposed by the characters of the singularity。 It is demonstrated to be useful in interpretation of Au anomaly in Gekou－Shicheng region Rushang Shandong Province 。 Based on the multifractal theory , Using the concentration—area（C—A）method ,We study two geochemical fields in Chifeng area , Inner Mongolia。The results show that the geochemical fields have three different multifractal modes。Based on these ,we discuss the enrichment mode of the geochemical elements and their distributions in space and get the anomaly lower limit ,then the geochemical backgrounds、regional anomalies and local anomalies are distinguished

The Pressure Transient Analysis Of Deformation Of Fractal Medium

The assumption of constant rock properties in pressure-transient analysis of stress-sensitive reservoirs can cause significant errors in the estimation of temporal and spatial variation of pressure. In this article, the pressure transient response of the fractal medium in stress-sensitive reservoirs was studied by using the self-similarity solution method and the regular perturbation method. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. The nonlinearities associated with the governing equation become weaker by using the logarithm transformation. The perturbation solutions for a constant pressure production and a constant rate production of a linear-source well were obtained by using the self-similarity solution method and the regular perturbation method in an infinitely large system, and inquire into the changing rule of pressure when the fractal and deformation parameters change. The plots of typical pressure curves were given in a few cases, and the results can be applied to well test analysis.